Ask Slashdot: Should More Math and Equations Be Used In the Popular Press?

raque writes "The NY Times recently published two op-eds in their Philosophy section, The Stone, discussing how Heisenberg's Uncertainty principle is abused. The second is a followup to the first. The author struggled to make clear his point and left the impression he was creating a strawman argument. In his followup he said he was avoiding equations because he was writing for a general audience. I replied to both articles, asking whether showing some basic equations would have worked better, allowing math to illustrate where metaphors struggled. Now I'm asking the same question to everyone on Slashdot. Would Dr. Callendar have been better off just diving in and dealing with Heisenberg and quantum mechanics using the tools that were developed for it?"

Comments

I just say

[Chrisq]

Probability that more maths equations should be used > 0

Re:I just say

[Spottywot]

Haha yes, of course people who are never exposed to equations are rubbish at reading them. It's a self-reinforcing feedback loop. I fear that the only way to get the general public to become more familiar with how to read equations would be to sneak them into sports coverage or something. Other than that my only other thought on the subject, is that surely anyone even a little bit interested in the Heisenberg uncertainty principle would be prepared to at least attempt equations and if not merely skim them and come back to them if needed?

Re:I just say

[Anonymous Coward]

It might be useful in some areas, but quantum mechanics... is one of the hardest places to start.

To put it another way, even if you introduce some equations for quantum mechanics, you are still going to look like an idiot compared to someone from the field... even someone from the field as it existed in the 1920s.

It might be better to go find experts in the field, and have them write short articles for the general public that are about established but not widely known things.

Re:I just say

[Anonymous Coward]

It might be useful in some areas, but quantum mechanics... is one of the hardest places to start.

To put it another way, even if you introduce some equations for quantum mechanics, you are still going to look like an idiot compared to someone from the field... even someone from the field as it existed in the 1920s.

It might be better to go find experts in the field, and have them write short articles for the general public that are about established but not widely known things.

I don't agree. People that read the NYT or other newspapers are not idiots. They have presumably attended school up to 12th grade and maybe even college. They should have as part of their general culture at least a "basic" understanding of maths.
So you can certainly write popoluar accounts of science using equations. The question therefore becomes how much is enough ? Now I don't think you can go as far as Roger Penrose did in Roads to Reality, that book even as a general science book is nearly unreadable.
On the other hand his previous 2 books, The Emperor's New Mind and Shadows of the Mind contain just enough basic quantum formulas so to at least understand some of the problems and solutions the author is describing in his book.
Authors that write for a layman audience are not writing for idiots, nor are they writing for 5 year olds. Show respect for your audience don't treat them like twerps. And popularizing science is difficult, so you have to find the right balance between metaphorical descriptions and equations. Go to far in one sense and you end up with a university textbook, go to far in the other sense and you end up with nonsense because all "physical informations" will have evaporated. Make things simple but no simpler. That's the magic and it's awfully difficult to achieve.

Re:I just say

[Anonymous Coward]

I don't agree. People that read the NYT or other newspapers are not idiots. They have presumably attended school up to 12th grade and maybe even college. They should have as part of their general culture at least a "basic" understanding of maths.

I think the parent referred to the fact that in Quantum Mechanics you can have the equations right and still talk nonsense. The point is that the equations alone don't say much. This is especially true for the uncertainty relation. For example, the position-momentum uncertainty equation and the energy-time uncertainty relation look quite the same, but their meaning is completely different (this is related to the fact that in quantum mechanics there is no such thing as a time operator).

Re:I just say

[Anonymous Coward]

Math != equations!! We need more actual math, AND less equations!

Here are some examples of actual math that I guarantee you *everybody* will love:
http://www.youtube.com/watch?v=VIVIegSt81k
http://www.amazon.com/gp/mpd/permalink/m1Z01590ONXHXN/

In fact here's a whole book of actual math that is so good at teaching math exactly because it doesn't focus on color-by-the-number "art" of training to use equations without actually understanding anything:
http://www.amazon.com/Measurement-Paul-Lockhart/dp/0674057554/
(I’m sure you've all read Lockhart's lament. This is the same Lockhart. And he put his money where his mouth is.)

Re:I just say

[chrismcb]

The probability you are wrong is > 0. If you are writing an article for mathematicians, include equations, If you are writing for non mathematicians then don't use equations. You need to speak in a language that the audience is familiar with.

Re:I just say

[AbsGeekNZ]

I would generally agree; but generally don't go beyond linear algebra; and in the wonderful modern age add a link or a QR on a printed article with links to improve understanding.

On these extra information sites have further links to more detailed information for those that are interested, further to this the same technique could be used with any technically dense subject matter...main artcle with basic scientific info ->link-> more in depth about original content ->link-> specific detail about relevant fields

Re:I just say

[Anonymous Coward]

I fear that the only way to get the general public to become more familiar with how to read equations would be to sneak them into sports coverage or something.

If there's one thing I learned, it is that the general public is able to memorize things facts related to an advanced concept, but they are not able to gain a deep understanding of said concept (e.g. why and how it works); they're 'users,' not innovators. Even something as simple as the Pythagorean Theorem is beyond the general public's comprehension, but they can easily memorize the actual equation and learn how to use it (e.g. "Do this, this, and this with this and you'll get the right answer.").

Re: I just say

[Anonymous Coward]

Actually the meanings are exactly the same. You have momentum as the translation generator for the position domain and the Hamiltonian as the translation generator for the time domain.

Re:I just say

[dywolf]

And you already confused something like 75% of the readership of a non-technical news source.

Re:I just say

[PopeRatzo]

I fear that the only way to get the general public to become more familiar with how to read equations would be to sneak them into sports coverage or something.

Brother, that's the truth. I've got a friend, teaches business statistics to undergrads, and is always surprised when one of her students, who are mostly dim on the subject, start spewing complicated statistical concepts that they picked up on sports radio, making the connection to stats more generally.

Now, statistics does not quantum mechanics make, but it's a start, you know?

Re:I just say

[Anonymous Coward]

I don't like pictures, I cannot even understand them. It's much much much much easier for me to have equations than a picture in almost all cases. I will most likely not be able to understand something complex mathematical without an equation.

And proofing prose text is far more complicated than proofing equations.

Re:I just say

[plover]

And that says more about our teaching abilities than our learning capabilities. The students are not necessarily dim, but they're not interested in the subject without an application they're also interested in. That's why a tutor is often able to help these people when a classroom lecture setting has failed - a tutor picks up on their interest and relates the subject to the student in a meaningful way. A small class size lets the teacher reach out individually as needed, whereas a large class will miss those students.

Does that mean we should offer "Advanced Statistics for Sports Fans II" and "Advanced Statistics for Theatre-goers II", etc.? Should we put max headcounts in classrooms? Or should we simply weed out those people who can't hack the lecture format? At what point should the education system start leaving children behind?

Re:I just say

[datavirtue]

I'd be happy with complete facts and the whole truth. Equations would bubble up to the surface every once in a while under those conditions. I stopped watching the news (TV) years ago because of the half-truth, spin, and bias on everything--just couldn't trust it anymore and didn't want to waste my time polluting my perception.

Re:I just say

[Robotbeat]

I would be opposed to any sort of calculus in an equation for popular press. But algebra? Yes. Algebra makes some things easier to understand.

And YES, it will require a little more mental effort for most people, but mental effort is a good gauge of how much someone is learning. In fact, put both the equation and a sentence explaining it. But algebra is sufficient for explaining the vast majority of physical concepts in a compact form.

Math equations are a language. A language we are all taught from middle school. We can and should use it, and use it clearly.

Re:I just say

[datavirtue]

I doubt most mathematicians really understand the Pythagorean Theorem. You get so used to theories and their application that you fool yourself into thinking you know them. Take manual long division or multiplication for example. We understand how to line up the numbers and perform the operations but prove to me that it works or *why* it works! There might be some 45 year old virgin with a severe intellect munching on DMT and living in his mom's basement somewhere in the world who can handle this but I think that most mathematicians would regurgitate meaningless crap they have been taught--offered as proof. As for me, I have no freaking idea where to even start proving these theories, but realizing *that* is half the battle.

Re:I just say

[datavirtue]

a tutor picks up on their interest and relates the subject to the student in a meaningful way.

What happens when they have no tangible interests?

Re:I just say

[Anonymous Coward]

Of course. That's the point; so few people understand the "whys" of math, and it's a problem. You don't have to be a secluded 45 year old virgin to understand it, though.

Re:I just say

[Talderas]

I think you should understand a little bit about vocabulary to understand the problem. "What", you may ask, "does vocabulary have anything to do with math and equations?" Well, first of all, equations are a very specialized form of vocabulary. A lot of formula are symbols which represent concepts. It's no different from a word. The context under which the word is used matters greatly in whether an individual becomes aware of a word which he or she does not understand. The word tectonic could be used to describe a smile in a fictional novel. Even though a read may not know what tectonic means it doesn't break the read out. On the other hand, if it were an article about tectonics, the word tectonic actually matters in the context and it becomes more visible to the reader that he doesn't understand the word however as the reader reads more and more articles about tectonics, even if he doesn't know what the word tectonic means, he will begin to not notice the words he doesn't know.

  So with equations, every symbol has a meaning and if the reader doesn't know that meanting the equation is nothing but illegible rubbish. Unless the New York Times regularly wrote articles that contained equations the average reader of the NY Times would be confused and skip the article. With a paper, like the NY Times, they want to keep the vocabulary used in all the articles (of a given section) in line with each other and more or less in line with the publication as a whole.

So the answer to the question in the summary is "No". He would not have been better off.

Re:I just say

[semi-extrinsic]

I think you are confusing mathematicians with engineers. Any mathematician worth his/her salt should know that the Pythagorean Theorem comes straight from the 2-norm in a Euclidean space, which is what most people mean when they say "the distance between two things". You can of course get philosophical and say, "why the 2-norm"?, but this is easily answered by an application of d'Alembert's principle. Now, you see what I did there? Yet another thing to figure out "why is it so", and indeed, you have to work fairly hard to find out how deep the rabbit hole goes.

Re:I just say

[michael_cain]

That's why a tutor is often able to help these people when a classroom lecture setting has failed - a tutor picks up on their interest and relates the subject to the student in a meaningful way.

That's a really good point. One of the problems with doing real-world examples in a general introductory college math class (ie, calculus, probability and statistics, >25 students) is that many of the subjects one might use require quite a bit of basic knowledge about the field that the example is drawn from. So we end up with the same tired old problems based on experiences that a majority of the students will have a grasp on.

Re:I just say

[Anonymous Coward]

It might be better to go find experts in the field, and have them write short articles for the general public that are about established but not widely known things.

The big problem here is that those who write well usually aren't good at math, and those good at math usually aren't that good with non-math written communication. You'll probably find few people skilled in both. Perhaps the scientist should write it up with the help of a professional editor. But at any rate, why NOT add the math? Those who can't understand the math can look it up or ignore it, those who are more numerate can gain insight they wouldn't get from mere words.

Re: I just say

[Anonymous Coward]

Then please tell me: What is the physical meaning of (a) Delta x, as it appears in the position-momentum uncertainty relation, and (b) Delta t, as it appears in the energy-time uncertainty relation?

Re:I just say

[drinkypoo]

And that says more about our teaching abilities than our learning capabilities.

It's not about abilities, but about approved methodologies. School isn't designed to advance learning for as many students as much as possible. It's designed to produce similarly-trained units which can be moved to the next stage of usefulness to those who went to expensive private schools for people in charge. Temp workers, soldiers, that sort of thing. No Child Left Behind — we will take them all to die in the desert.

Does that mean we should offer "Advanced Statistics for Sports Fans II" and "Advanced Statistics for Theatre-goers II", etc.?

If these classes can cover useful material and appeal to sufficient numbers to have asses in seats with heads above them learning? Yes.

Should we put max headcounts in classrooms? Or should we simply weed out those people who can't hack the lecture format?

There is clearly a need for educational institutions which are capable of teaching to the individual student. Their lack is a factor of the structure of our society. Though we now produce plenty for everyone, we insist that people whose output is no longer necessary (nor, apparently, desired) are useless and that there is something wrong with them. Yet, society exists to serve its members, and not the other way around. If society produces unwanted members, it is society which has failed, not those individuals. But if your basic welfare were not tied to your productivity, then many people who now are forced to scrap and scrape to survive might have the time to make a positive contribution — perhaps even in education. But this is a matter of priorities — When we have corporate bailouts but not student loan bailouts, and yet permit CEOs of companies receiving bailouts to pocket massive bonuses, we not only declare but prove what our government's function is — to provide opportunities for rich people to become richer at the expense of all others. If we cared about the future, we'd show more care for education. Not with unfunded mandates and leading from the stratosphere, as exemplified by NCLB, but with a system which permits more individual attention.

At what point should the education system start leaving children behind?

Since we have an abundance of most sorts of tradesmen (there is little point today in becoming an electrician or a plumber) the answer really ought to be only when it is impossible to raise their interest. I believe that different people have different capacities, but I also believe that most people are operating well below theirs. Investment in education pays many dividends. Who is well-paid by investment in war?

Re:I just say

[Trepidity]

Putting a probability on a normative claim being true is interesting. You must be one of them Bayesians.

Re:I just say

[Russ1642]

Because the math you see in sports coverage is excellent already? They abuse statistics like a misbehaving mule.

Re:I just say

[PopeRatzo]

I don't know. I think the best way to invest in education is to invest in good jobs for parents. When the downward pressure on the lowest 2/3 of the economic scale becomes so great that it breaks up families, causes young people to give up on society, it makes it impossible to have the kind of family structures that create the highest possibility of children entering school with their interests already raised.

By trying to treat the problem at the school-level, we're just medicating the symptom, not dealingi with the underlying disease. That's why I think the effort to pour money into pre-school education completely misses the point. Those kids have to go home sometime.

Re:I just say

[plover]

As a teacher, I try to relate my lectures to their specific interests (I know one is into motorcycles, one works at a bank, etc.) or prior history (over half of my current students were in the military.) Otherwise, I try to relate them to either my day job or to the job market the students will be entering. "When I'm hiring, I look for people who have demonstrated X on a past project. That tells me they have practical skills working with Y and Z. So lets talk about Z for a while, and why it's important."

That's obviously easier to do on a technical topic related to their field of choice than it would be for a generic topic addressed to an entry-level group of students. How a teacher could relate the lessons of the battle of Gettysburg to students interested only in The Next American Idol would be a lot more challenging.

Re:I just say

[Immerman]

You suddenly realize you got lost in thought and wandered off campus, and are now lecturing to a rutabaga.

Everybody has interests, and math being math almost all interests can be tied back to it if you're halfway clever. If you are completely unable to establish the rapport
necessary to discover those interests for most students, or are unable to link those interests to math, well then perhaps you should reconsider your decision to teach.

Re:I just say

[Anonymous Coward]

I don't agree. People that read the NYT or other newspapers are not idiots. They have presumably attended school up to 12th grade and maybe even college. They should have as part of their general culture at least a "basic" understanding of maths.

People who edit and typically write for the NYT times on the other hand....

Re:I just say

[Immerman]

Indeed. Perhaps it would be more productive if we stopped teaching introductory math classes, and instead taught introductory sicence/math hybrid classes. I got my introduction to both linear algebra and differential equations within engineering classes that needed a bit higher math than the students could reasonably be expected to have had at that point - as a result the engineering portion of the classes lost a week or two of topical lecture time, but we learned the mathematical basics in the context of actually using them to solve real-world problems. When I eventually took the specific math classes I was already comfortable with the usefulness and "flavor" of the math, and the class was essentially fleshing out a skeletal understanding with all sorts of more powerful and esoteric details.

Re:I just say

[mwvdlee]

Write the equations out on a chalkboard and make a picture of it.
Those who understand the equations, can read them and understand.
Those who do not (which, for quantum mechanics, probably includes me) still have a pretty picture of sciency math scribbles on a chalkboard.

Re:I just say

[zildgulf]

I would agree that most people cannot read equations to save their lives, especially in the US. The haphazard way teenagers are taught and learn Mathematics in the US, especially Algebra, makes it difficult to put anything more mathematically difficult than Roman Numerals, fractions, and percents. Even then there are millions who can't even comprehend these things as evident in other internet forums. That creates a self reinforcing loop.

Maybe a good start is the most basic practical rules of thumb in finance since more people are focused on money rather than math. For example the rule of 72, which predicts how many years it will take to double your money at some interest rate. The equation would be written for the layman as 72/(interest rate) = Years to double your money.

Re:I just say

[zildgulf]

I think you are confusing mathematicians with engineers. Any mathematician worth his/her salt should know that the Pythagorean Theorem comes straight from the 2-norm in a Euclidean space, which is what most people mean when they say "the distance between two things". You can of course get philosophical and say, "why the 2-norm"?, but this is easily answered by an application of d'Alembert's principle. Now, you see what I did there? Yet another thing to figure out "why is it so", and indeed, you have to work fairly hard to find out how deep the rabbit hole goes.

And Joe Plumber looks at this quote and says "What the h*ll is he talking about?"

Re:I just say

[tlhIngan]

The big problem here is that those who write well usually aren't good at math, and those good at math usually aren't that good with non-math written communication. You'll probably find few people skilled in both. Perhaps the scientist should write it up with the help of a professional editor. But at any rate, why NOT add the math? Those who can't understand the math can look it up or ignore it, those who are more numerate can gain insight they wouldn't get from mere words.

Or, besides writing down the equation, EXPLAIN the equation. And not just write down what the equation says, but what it means.

Let's take a simple one - E=mc^2.

It says the amount of energy something contains is related to its mass (or the amount of "stuff") it contains. The relation is a big one - it's equal to the speed of light squared, so a tiny amount of mass (stuff) produces a LOT of energy. This equation is fundamental to nuclear physics, including peaceful uses such as nuclear power plants, to destructive uses such as nuclear weapons.

Thus the paragraph put close to the equation helps those who can't read the equation to still understand what it says, and it also explains where it's used and what it means.

But you're correct on the fundamental problem - it's because those in the sciences (and engineering) put little weight on the "arts" side of things (including things like writing) as they believe that stuff is a lot of fluff. (I can't generalize this, but if you ask a lot of people in IT, they seem to look down on studying anything that isn't related to their field - like why should a computer scientist or engineer take courses in philosophy or logic, or take classes in English or writing or even home economics).

Likewise, a lot of people take arts because they want to avoid the math and science.

Which is terrible - and it leads to this gulf of communications problems where journalists (or any writer, really) misinterprets some scientific or technical thing because the writer and the technical person are failing to communicate effectively (a problem on BOTH sides). Or how technical people look upon sales, marketing and PR people with disdain, because those people know how to relate to the public, but often fail to relate to the technical staff.

Perhaps instead of the token math or science class for an arts degree, or the token arts/business class for a technical/science degree, the two should be combined more tightly to produce a more well-rounded person who may be technical, but understands the other side.

Re:I just say

[Immerman]

I cannot have a meaningful discussion about the subtleties of snow except in something like the Inuit language that has a suitable vocabulary for the topic. Similarly you can't have a meaningful discussion about a scientific topic without using a language with a suitable vocabulary - which generally speaking means mathematics. Sure you can write fluff pieces that might give the hypothetical layman a vague sense of the shape of the discussion, but it's like grilling up a side of AAA beef, and then just licking the crust.

And really there's no reason for anyone not to be able to understand at least algebra, except that we tend to teach it in the most difficult, arbitrary, and generally useless and overcomplicated format possible. Maybe that will start to change now that we have cheap machines that can easily do all the ruthlessly pedantic "solve for X" portion of the work (at least at the algebraic level), so we can focus our general education on using it as a language instead. All word problems, all the time - if you can properly express it in mathematical language then the computer can do the rest. Of course we'd still need some classes on how to do the actual heavy lifting for those who wish to explore the boundaries of mathematics, call it "Equations for Mathematicians" and fill it with students looking to become mathematicians, theoretical physicists, etc.

Re:I just say

[Anonymous Coward]

Wider understanding of math would also help silence atheists, since quantum mechanics proves that dogs have souls.

The mathematical proof can be found here.

Re:I just say

[Anonymous Coward]

What??? A mathematician is exactly who would be able to answer those questions. Also weren't all of those proofs done hundreds of years ago? Secondly what a mathematician does and "math" to every other profession is not the same, theoretical math and full proofs for things like 1+1=2 is not going to be a hurdle or even necessary for most people. In college they barely mentioned DeMoivre's theorem, even in classes which used its applications, it's simply unnecessary.

Re: I just say

[Anonymous Coward]

If you insist. Assume for simplicity that the mean values are zero (keeps calculations more compact and you can always do a shift if you like to put the origin of the axis in an arbitrary position). Integrals are over the whole domain.

(\delta x)^2 = \int x^2 \phi(x)\phi^*(x) dx -> mean square deviation from average

(\delta t)^2 = \int t^2 \phi(t)\phi^*(t) dx -> also mean square deviation from average

To be more specific. In this formulation (picking a basis for the state vector), you derive the position-momentum relation starting from the obvious:

\int | \lambda x \phi(x) + d\phi(x)/dx |^2 dx >= 0

and treat it as a quadratic equation in \lambda that's required to have at most one root.

Now, since momentum is the shift generator for the x translations, you will eventually replace (d/dx) with (i\hbar p). That, together with the trivial commutation of x and d/dx gives you the uncertainty relation.

Repeat the procedure with t instead of x. Bearing in mind that -H is the generator for time translations, you'll end up replacing (d/dt) with (-i\hbar H) which will give you the other uncertainty relation.

Happy?

Re: I just say

[Anonymous Coward]

He asked for the physical meaning of it and you merely elaborated on the maths. Try again.

Re:I just say

[Kelbear]

http://en.wikipedia.org/wiki/Uncertainty_principle

The formulas in question are laid out in this link.

I took calc I, calc II, and linear algebra in college so I have a literate, but nonetheless layman's understanding of math.

The problem with explaining these subjects through formulas is that though I recognize the syntax being used, there are a WHOLE LOT of variables presented, with minimal explanation of what each variable represents. Where an explanation is given, it is primarily a link to an underlying wikipedia article because the explanation of what that variable represents is a non-trivial undertaking. But I'm not trying to say that the wiki articles are bad.

It's a complex topic, and there's only so many details you can shave off of a subject until you lose important details and start to misrepresent the mechanics. The wiki article is aiming at an accurate technical explanation, with layers of depth for those who have the time, while a newspaper article needs to communicate a concept to those who have very little time (if they actually had time, they would be doing some real study on the matter rather than just skimming a newspaper article).

The newspaper article and the detailed wiki article serve two different goals and should be taken in conjunction with one another. The newspaper article gives just enough information to entice a reader to learn more, at which point the wiki article can step in (or any other more detailed resource).

Bottom line: No, I don't think more math and formulas should be used in popular press. Complex math has upper limits of simplification, and the goal of public press articles is to foster curiosity through concise communication.

Re:I just say

[Anonymous Coward]

I doubt most mathematicians really understand the Pythagorean Theorem. You get so used to theories and their application that you fool yourself into thinking you know them. Take manual long division or multiplication for example. We understand how to line up the numbers and perform the operations but prove to me that it works or *why* it works! There might be some 45 year old virgin with a severe intellect munching on DMT and living in his mom's basement somewhere in the world who can handle this but I think that most mathematicians would regurgitate meaningless crap they have been taught--offered as proof. As for me, I have no freaking idea where to even start proving these theories, but realizing *that* is half the battle.

Wow. Long division and manual multiplication are just applications of the distributive law. As for the Pythagorean Theorem, perhaps not off the top of one's head but a mathematician would certainly be able to find a proof that they could explain to you (http://www.cut-the-knot.org/pythagoras/index.shtml).

Re:I just say

[Hotawa Hawk-eye]

Equations are one piece of the puzzle. Words are another piece. Pictures or examples are a third. Using one of the pieces alone may not be enough; using two or all three, if done well, could be better.

For instance, in explaining E = mc^2 you could explain it in words: the amount of energy that would be released if a small piece of matter, say 1 gram, is enormous. Or you could give the exact amount of energy produced. Or you could show a collection of Olympic size swimming pools and indicate by how much it would heat the water they contain using a graphic of a thermometer. E = mc^2 on its own doesn't really paint a picture in readers' minds of how much energy that actually is. Even the number, without some sort of context, doesn't really do it justice. But most people have some idea about how big an Olympic sized swimming pool is, and can tell that it would take a lot of energy to heat it. If you say "turning one gram of matter completely into energy would take 100 Olympic swimming pools from just above freezing to just below boiling" (pulling that figure mostly out of thin air) that's something a lot of people can picture.

Re:I just say

[Marxist Hacker 42]

I'm not so sure. Having read a better description of the Heisenberg Principle in this article than I have ever seen before, it should be theoretically possible to now build a Heisenberg Compensator, which was impossible in 1920 but is completely possible now. If you know the amount of energy in the photon taking the picture of the electron, then it should be possible to use software and a very fast computer to accurately record the position and velocity of every electron in any given system. It will take a massive amount of redundant processing, but it is POSSIBLE to compensate for the uncertainty principle. Same goes with any other form of measurement- first feed your model into computer memory, then adjust for the effect of the measurement in the model.

Re:I just say

[zAPPzAPP]

I would expext that anything that could be expressed in a simple enough equation, could also be described in words easily enough.

But the first example in the summary mentions the Heisenberg uncertainty. Concepts like this are hard to describe in words, but the equations are just as hard to grasp. They are usually completely made up of often obscure variables, each of them standing for another equation, or an abstact concept of its own.
Unless you happen to know each of these, you will not be able to make much sense of the complete equation.
Trying to discover their meaning will quickly lead to even more unknowns for anyone not yet familiar with the topic.

Most people understand the language of the equation itself, which describes the relation of it's parts to each other, But if the parts of the equation are unknowns, how much use is that?

Re: I just say

[Anonymous Coward]

Mean square deviation is the physical meaning. Unless you're asking for a macroscopic equivalent which would be utter nonsense at this level. Thanks for playing anyway.

Re: I just say

[careysub]

I believe he was asking how it applied to cars.

Re:I just say

[Anonymous Coward]

It is indeed easy to prove the Pythagorean theorem for a vector space with a 2-norm. It is an easy calculation. But it is not at all obvious why the space we live in can be described accurately as such a space. We can show that by starting from the more intuitive Euclidean axioms or their modern day version stated by Hilbert. Then the Pythagorean theorem has a beautiful, non-obvious proof. Of course, when we make claims about the space which surrounds us we also enter the realm of physics: to check the axioms we need to make measurements, like checking the sum of angles in a worldly triangle.

Re:I just say

[Anonymous Coward]

I disagree. If the goal were to have all readers understand what you're writing, I might agree. But sometimes it's enough to have the reader understand that there is a complexity to the topic that they're just not going to be able to grasp.

For instance, I wonder whether so many people would chime in and challenge the views of climatology scientists if more of the arguments included the complex math involved in the science. A native with a blow gun won't know he's outgunned by a marine with an M-16 until the marine fires off a few rounds and shreds something. Similarly, technical articles should fire off a few equations so that laymen understand both the gist of the topic from the words in the article and just how far beyond them the subject is from the equations.

Re:I just say

[Darinbob]

Except that this is harder than the surface. The units matter greatly. It works out because metric units are defined using other metric units (ie, gram was originally the mass of an amount of water in a cubic centimeter). If you change the units it doesn't work out; ie, using watts, pounds, feet, and hours. Or even if you use kilograms versus picojoules. C^2 is only a huge number if you use small units, it's not nearly so big if you use parsecs per hour.

What's more interesting than the constant used is the math used to derive the formula, and what that math implies, and the related equations involving rest mass or relativistic mass, or what happens with massless particles. But that's extremely complex, beyond lower division university physics. It really only caught the public's eye because it's a simple formula and easy to remember, no weird mathematical symbols or Greek letters, and constants based on things that can be related to.

Re:I just say

[Phase Shifter]

It might be better to go find experts in the field, and have them write short articles for the general public that are about established but not widely known things.

I'm not convinced. In principle it sounds great, but in practice you'll have a lot of resistance coming from several different groups:

)1) Christian fundamentalists who have no room for uncertainty in their model of the universe. To them, you might as well be reading from the Necronomicon, because anything that's unknown can't be declared true, anything that isn't true must be a lie, and all lies come from Satan.

2) New age crystal wavers who are still convinced that quantum mechanics proves there are many celestial planes (many worlds interpretation), sympathetic magic really works (entanglement), and that reality is shaped by our consciousness (Copenhagen interpretation). Never mind that the associations they make are utterly baseless, and the interpretations they're based upon actually contradict one another to some extent...

3) All the people who got sold on poorly written work that was dumbed down "for the public" in the past, (Pretty much anyone who's convinced that entanglement means FTL communication and Star Trek-style teleportation are just around the corner)

What's in common here? These people think they already know, and your attempts to enlighten them will initially only reveal how confused they are. This works aqainst you, because for them certainty and truth are not objective (but abstract) measures of how well a theory does or doesn't work, but feelings... and you just made them feel uncertain/bad, so what you are telling them is "less true than what they already know", which makes you clearly a "Satanic deceiver" / "conspirator suppressing the truth" / "clueless idiot who didn't read the Quantum Physics for Complete Morons sidebar in their favorite gaming magazine last month".

Not to say this isn't worth doing, just that you need to set your expectations very low.

Re:I just say

[StripedCow]

Let's take a simple one - E=mc^2.

It still does not make sense. What do you mean by "contains energy"? Something may contain a gazillion Joules, if I cannot get the energy out, then that means nothing to me. If I have a heap of bricks of mass "m", can I even use them to power my wrist watch?

Then, the uncertainty principle. It seems really difficult to apply in an actual situation. Is that law even used in simulators for quantum mechanical systems? It really makes little sense, even if knowing the equation. It is almost like reading "if a pony shows up on the scene, gravity is reversed". How am I supposed to evaluate that rule? To what exactly does it apply? How do I put it in a simulator?

Until popular science explains stuff in more clear terms, I'm not reading any of it any longer.

Re:I just say

[reve_etrange]

No, the uncertainty principle is not due to technological limitations. The uncertainty relationship is a fundamental property of all phenomena characterized by finite-length wave trains, quantum mechanical or no.

I paraphrased Feynman's explanation as well as the mathematical reasoning in another comment

Feynman sez:

Here we encounter a strange thing about waves; a very simple thing which has nothing to do with quantum mechanics strictly. It is something that anybody who works with waves, even if he knows no quantum mechanics, knows: namely, we cannot define a unique wavelength for a short wave train. Such a wave train does not have a definite wavelength; there is an indefiniteness in the wave number that is related to the finite length of the train, and thus there is an indefiniteness in the momentum.

Re:I just say

[Phase Shifter]

I don't agree. People that read the NYT or other newspapers are not idiots. They have presumably attended school up to 12th grade and maybe even college. They should have as part of their general culture at least a "basic" understanding of maths.

People who edit and typically write for the NYT times on the other hand....

I take it you don't live in a state where anyone has tried to drag the "ID vs. evolution" issue into political debate recently. The problem is that for most people "true" means "I want to believe this", not "This can be independently verified".

Re:I just say

[DMUTPeregrine]

You seem to misunderstand the source of the uncertainty in Heisenberg's principle. The unknown energy of the photon (or other observation method) is not the source of the problem, it's inherent. The Fourier uncertainty principle relates any function and its Fourier transform. The more concentrated a function is the more spread its Fourier transform, and position and momentum in QM are related by the Fourier transform. So the more precisely you measure the position, the less precisely you know the momentum.

Re:I just say

[multimediavt]

I am gonna up the ante a little and say that a large number of "journalists" have trouble writing in their own language properly. Now, you want them to learn math when they can't even write a complete sentence? Hahahaha Oh, and then there's the "editors" who are supposed to check these things and correct the writers. Yeah, that doesn't happen with words and you want/need them to correct (possibly) complex math equations. Puh-lease.

Re:I just say

[idontusenumbers]

Or how technical people look upon sales, marketing and PR people with disdain, because those people know how to relate to the public

Do marketing and PR people really know how to relate to the public? I find most marketing and PR is a gamble. Countless super-expensive campaigns are utter failures (for a particularly good example, see the Tropicana Packaging debacle, or the recently revealed poor sales of Windows RT tablets). They might be better at relating to the public than technical people, but even the best firms are just throwing darts at a dart board. Some campaigns are great, but most are just lost in a sea of similar monotony or are complete disasters.

Re:I just say

[Anonymous Coward]

I cannot have a meaningful discussion about the subtleties of snow except in something like the Inuit language that has a suitable vocabulary for the topic.

You aren't trying hard enough.

Re:I just say

[maxwell demon]

But it is not at all obvious why the space we live in can be described accurately as such a space.

But that's not a question of mathematics, but a question of physics.

Re:I just say

[narcc]

I take it you don't live in a state where anyone has tried to drag the "ID vs. evolution" issue into political debate recently. The problem is that for most people "true" means "I want to believe this", not "This can be independently verified".

Still fighting the civil war? It's time to move on. The battle was won ages ago. The only ones still fighting it are the odd evangelical and the science cheerleaders.

Just let it go, man. Just let it go...

On truth, I should probably point out that science does not deal in truth. Science neither offers nor tends toward it. It is, in fact, antithetical to science. You will never hear "science says that x is true" from anyone who has a basic understanding of science.

I know that it's useful for fighting against the enemy in your imaginary creation/evolution war, but distorting the very nature of science can only hurt the public understanding of science.

Re:I just say

[Marxist Hacker 42]

So the real problem is that the Heisenberg uncertainty principle isn't about either position or velocity, but frequency?

Still should be able to compensate for it by running two parallel processors, one working on concentrating the function for position, and the other working on concentrating the function for momentum, thus giving TWO Fourier transforms.

Re:I just say

[Marxist Hacker 42]

Once again, looks to me like a data measurement problem, not an inherent problem. A short wave chain in this case is fewer data points than are needed to calculate the wave frequency because you don't have enough peaks. But what if instead of one detector, you have a million? Instead of one processor doing the fourier transform, two million cores, each either working on position or momentum, using a different sensor?

Like I said before. Hard is not impossible. It's just a matter of figuring out how to get more data.

Re:I just say

[Anonymous Coward]

But you're correct on the fundamental problem - it's because those in the sciences (and engineering) put little weight on the "arts" side of things (including things like writing) as they believe that stuff is a lot of fluff. (I can't generalize this, but if you ask a lot of people in IT, they seem to look down on studying anything that isn't related to their field - like why should a computer scientist or engineer take courses in philosophy or logic, or take classes in English or writing or even home economics).

In the sciences, we have a name for people that are bad at explaining things in writing -- shitty scientists.

Not sure what you figure home economics has to do with it, though.

Re:I just say

[DMUTPeregrine]

No, it's an inherent mathematical problem related to the way quanta work. There are no particles, just quanta. Quanta are represented by wave functions, which is where the uncertainty actually lies. Doing rapid alternating measurements of position and momentum doesn't help, as it's still not the position and momentum at the exact same time. Simultaneity is a tricky concept, and even if you had a perfect frame of reference for it you'd still have the two measuring systems interfere with each other. Even if they didn't it would still be impossible, because the underlying problem isn't that you can't measure the momentum well if you know the position exactly, it's that the momentum becomes undefined. Likewise, if you know the momentum exactly the quantum will have no defined position.

Re: I just say

[smaddox]

Lets do the calculation:
E = m*c^2 for m = 1 gram yields ~2e13 calories
An Olympic pool has a volume of ~2500000 L = 2.5e9 mL
Dividing the two yields a temperature increase of 8000 Celsius, which is enough to turn water just above freezing point into a plasma.

There's far more energy locked up in the form of matter than is even comprehensible.

Re:I just say

[Anonymous Coward]

Probability that more maths equations should be used > 0

I find that the general public doesn't even know which one of these symbols means less than, and which one means greater than: > <

Re:I just say

[semi-extrinsic]

No doubt. But the post I replied to was talking about "most mathematicians", not Joe Plumber.

Re:I just say

[Anonymous Coward]

Well, for me it's the exact opposite. And I am a programmer.
Diagrams just make sense. Equations are opaque and encoded. I don't like the actual steps of 1. guessing what those weird one-letter symbols actually are in that particular context (a stupid and pointless game in an of itself), 2. always being forced to go the indirect way, by having to actively keep in my head, that "upside-down triangle" is a function that when applied in this special way actually means this function full of meaningless symbols which I *also* have to translate, and in that other way, is *a completely different* function full of meaningless symbols which I *also* have to translate, and when applied in *yet* another context... GAAAHHH!
WHY FOR FUCK'S SAKE DON'T THEY USE THE THING DIRECTLY INSTEAD OF THE MOST OBFUSCATED SYMBOL ANYONE COULD EVER COME UP WITH THAT "REPRESENTS" THE THING?
My thought process is too fast and my picture too big, to waste time and brain power with that shit. It forces me to be small-minded and jump through miles of boilerplate hoops. Not acceptable!

Also @ all mathematicians: USE DESCRIPTIVE IDENTIFIERS, FOR FUCK'S SAKE!!

Re:I just say

[Marxist Hacker 42]

You clearly don't understand what I'm saying. I'm saying if you know all the properties of both measuring devices, you can correct for the error in the quanta. The experimenter doesn't have to know both at the same time, the computer network can.

Re:I just say

[rioki]

What you propose will not work. The reason being that measurement on a quantum level, actually on almost all other, is destructive. Imagine you want to measure the speed of a train by bouncing cannon balls off of it. One cannon ball will not derail a train, though it will have a severe dent. What you are proposing is to fire thousands of cannon balls at it. Although you may have determined the position and speed of the train, there will not be a train left. In addition your later measurements will be altered by your earlier measurements rendering the later ones inaccurate to it's initial state.

Re:I just say

[Marxist Hacker 42]

Yes, but measurably inaccurate.

My original off the cuff troll on this subject referred to Heisenberg Compensators. Those who can correctly identify where these are used in a certain science fiction series, will recognize that the original is *always* destroyed, and an exact duplicate created elsewhere.

Re:I just say

[david_thornley]

Is your idea to capture photons that may have bounced off the electron, and use them to determine position and their momentum/energy transfer to determine momentum at that point? It seems to me you'd have to know the photon energy at the point of detection, which is pretty much the same thing as knowing the photon's momentum and position to arbitrary precision. It would appear to be Heisenberg compensators all the way down.

Re:I just say

[reve_etrange]

Well, that may not be true. It would seem that when the transporter is operating normally, the original matter is in fact sent. We even see a first person view which is uninterrupted during transport. On the other hand, under special circumstances some people are able to use the transporter to make duplicates or new individuals from patter buffer records (i.e. Data makes a new Picard at one point).

Obviously there is a healthy debate on this subject.

Re:I just say

[reve_etrange]

It doesn't matter how many sensors you have or how large or small the wave train is. The "uncertainty" is a fundamental component of all wave-like phenomena with finite extension. For these phenomena there exists only distributions of the variously "uncertain" parameters (e.g. frequency, momentum), which may be sampled by measurement.

Consider an infinite sine wave of a given frequency. Multiply this with a Gaussian to obtain a wave train of finite extension. Now, if you Fourier transform the wave train in order to measure its frequency, you will have the Fourier transform of the sine - a delta function - convolved with the Fourier transform of the Gaussian, itself a Gaussian. This leaves you with a Gaussian in frequency space and thus no definite single frequency. The continuous Fourier transform is used so the result can not be due to discretization effects.

Re:I just say

[reve_etrange]

The point that the uncertainty principle applies only to simultaneous measurements is critical. Obviously you can make separate measurements of speed and position at different times!

Nevertheless, it is not necessary to invoke destructive measurement to explain uncertainty, because as I said the uncertainty relationship is a necessary feature of any wave-like phenomenon of finite size. It's not just that measurements of parameter require destructive interactions with the system, but that a single true value of the parameter does not exist.

Re:I just say

[Marxist Hacker 42]

Yep, the question is does it diverge or converge? Otherwise, this is just the same as the iterative method of solving an integral.

Re:I just say

[Marxist Hacker 42]

Replace the continuous Fourier Transform with an iterative Fourier transform, with multiple measurements of the finite wave train, then average is the basic idea. The more samples you have, the more correct will be the single frequency that comes out. "No definite single frequency" is not equal to "no discoverable single frequency"/

I'm not saying it will or won't work. I'm saying that it is fundamentally impossible without significant processing power. Processing power that we're coming closer to possessing than we had in 1920.

Re:I just say

[plover]

That's a really good point. Much of the violence we still see in the world is due to cult leaders whipping up the sentiments of some truly impoverished people, and using them as "holy warriors". It's a role they're happy to take on because they literally have nothing else; and what could be better than an important man who says God himself wants them! (Trick question, the right answer is "a steady job and food on my family's table", but a charismatic leader never permits his followers to use logic to arrive at the correct answer, he always claims his book provides "all the logic you need.")

Instead of giving bales of money to the Pentagon, we could have used that same money to build tens of thousands of worker-owned factories across Iraq and Afghanistan, and given their people jobs and income instead of reasons to blow themselves up. It sure would have cost the U.S. taxpayers a lot less, and would have led to a more sustainable peaceful outcome. Think of it as the Marshall Plan executed thousands of times at the mosque level, instead of once at the Emperor's level like we did in Japan after WW2.

So to get back to America, creating public works jobs (like the Works Progress Administration did back in the first Great Depression) would be one way to get people feeling valued, and getting value out of them. And that's going to lead to stability.

Re:I just say

[Occams]

Commercial media is always dumbed down to the mentality of the kind of people who will respond to the advertising. Math is not good sucker-bait.

Re:I just say

[DMUTPeregrine]

There are no errors. The quantities cease to exist in any meaningful sense. The computer network IS an "observer" for the purposes of QM.
Heisenberg's uncertainty principle is just an application of the Fourier uncertainty principle to quantum wavefunctions. You have to find a way around the Fourier uncertainty principle to find a way around the Heisenberg principle.
A simple example:
If we have a function (say, probability that a particle is in a location in 1 dimension) that is zero everywhere except over some interval, where it's a constant value less than 1, then we can represent the position probability with a rectangular function. The momentum is the Fourier transform of the position function, so it will be a sinc function. The narrower the rectangular function (fewer possible positions) the wider the sinc function (more possible momenta.) In the ultimate case, one would know the position exactly, the rectangle would have no width, and you'd get a delta function for position. The Fourier transform of a delta function is a constant value, so for a perfectly known position the particle would have all possible momenta, at the same time. The reverse is also true, for a perfectly well-defined momentum the particle would be "spread out" over the entire universe at once*.

* Planck's constant actually provides a limit on how precisely you can know either value, so they don't go to infinity, but they do "spread out" as described.

Re:I just say

[reve_etrange]

Replace the continuous Fourier Transform with an iterative Fourier transform

It doesn't matter. The discrete transform approximates the continuous transform; in the case we're discussing we can in fact calculate the continuous transform analytically. If one were to use the discrete transform with an explicit numerical example basically the same result would be obtained (down to numerical error modulo the window function, zero padding and discretization artifacts). That result being a distribution of non-zero amplitudes in frequency space rather than a delta function.

"No definite single frequency" is not equal to "no discoverable single frequency"

There is no single frequency, discoverable or otherwise. The physical reality is that a finite wave packet such as a shout or an electron must be characterized by a distribution of frequencies rather than a single frequency. It is impossible for a single frequency alone to produce a finite wave train. There are two ways to get a finite wave packet, either you have a window of some kind, which creates overtones in the frequency space, or you sum up lots of higher frequency waves, which amounts to the same thing.

The whole reason I brought this up is relevant to TFA: in my opinion the above approach gives the simplest, most accurate portrayal of why the uncertainty relation is a part of nature and not a technological limitation of some kind (we aren't "missing" any information which actually exists). To reiterate: 1) regardless of quantum mechanics, finite wave-trains create "uncertainty," that is a distribution of values which may itself be known exactly, and 2) quantum mechanical systems are finite wave phenomena. Therefore they exhibit what we call "uncertainty" - a distribution of values which can be sampled. Repeated sampling demonstrates that quantum mechanics predicts these distributions with extreme accuracy and precision.

Anyway, uncertainty is actually an important part of quantum mechanical technologies, more than a barrier. Especially in living systems, which use QM in various ways.

Re:I just say

[Anonymous Coward]

Perhaps instead of the token math or science class for an arts degree, or the token arts/business class for a technical/science degree, the two should be combined more tightly to produce a more well-rounded person who may be technical, but understands the other side.

They talk to the customers so that the engineers don't have to...

Another place where the same lack of general understanding shows up is with relativity. Both quantum mechanics and relativity take mental effort to be understood at more than a superficial level.

Betteridge

[Anonymous Coward]

Betteridge's Law of Headlines says no.

Re:Betteridge

[Xest]

Do you have an equation to back that law up?

Re:Betteridge

[hweimer]

Betteridge's Law of Headlines says no.

And at least in this particular case, "no" is indeed the correct answer. Equations can never be a substitute for actual understanding. You can use equations to develop understanding by starting from an earlier point and transform the initial equation to establish a new fact. But where do you start with quantum mechanics? "Quantum states are being represented by rays in a complex Hilbert space"?

If anything, equations can be used to create an argumentum ad auctoritatem, and I'm not sure that this is a good thing.

Re:Betteridge

[Anonymous Coward]

Wait while I resubmit it as "Is there enough math and equations and popular press?"

PS: Betteridge's law doesn't work that way. Be so kind and GDIAF with other parroting it in all the wrong topics.

Re:Betteridge

[Anonymous Coward]

If anything, equations can be used to create an argumentum ad auctoritatem, and I'm not sure that this is a good thing.

Next article: "Should more Latin be used in articles? Or will it just confuse people not normally exposed to it?"

Re:Betteridge

[StripedCow]

Let H be the set of all possible headlines.
Let Q be the set of all strings ending in a question mark.
Let E[v,U,t,p] denote the evaluation of natural language question v, where E[v,U,t,p] in { TRUE, FALSE, UNDEFINED }, and where evaluation is performed in universe U and at time t corresponding to position p. Let T(U,p) be the function that returns the time of a given universe U at a specified position p.

Then, for all v in intersection(H,Q), for all U, for all p in U, and t >= T(U,p), it holds that E[v,U,t,p] = FALSE.

The proof is left as an exercise for the reader.

Of course, I should have used a formal language to write down this assertion, but it would have taken me at least a week, so I took the cheap and easy route of using prose, like all mathematicians do, by the way.

Disclaimer: IANAM (not a mathematician)

Why bother?

[Anonymous Coward]

You can use them all you want. It won't make people any smarter or able to understand them.

Hell doing so might even cost you viewers/readers. people don't like things that make them feel stupid.

Re:Why bother?

[Sockatume]

You'll make people smarter and able to understand the subject if you explain what's going on in the example you want to discuss. That's a pretty basic idea in writing popular science.

Re:Why bother?

[Mikkeles]

One should bother because pandering to the lowest denominator will ensure that most will meet that expectation.
There is a range of happy media between a wall of mathematical formulae and proofs and an awkwardly written, purely textual interpretation. Not everyone will have a full (or even good) comprehension of the meaning, but those willing to be challenged will have something on which to proceed.
Those who don't care or who like pap can just move on to the latest on Kate and William (who, I believe, just had a baby or something).

It's a newspaper.

[Anonymous Coward]

Newspapers intentionally and consistently use language that does not require a master degree in English language to understand. So where is the point in writing an article that requires a PhD in physics for understanding?

Just point out the conclusions of the scientists.

NYT's Science Going Downhill

[Anonymous Coward]

The science reporting of NYT is really going downhill. A year or two ago an article like this would never have been posted.

You can't write about quantum mechanics without equations - it is NOT an intuitive field.

Disclaimer: I'm an otherwise pleased, and paying, customer of NYT. I have no other relation to them. I was fucked in the ass by a goat yesterday.

Re:NYT's Science Going Downhill

[Sockatume]

You can write about the results - which is important - but you can't write about the mechanics without at least describing the mathematical concepts and their relations with physical reality. This is why it's such a problem, because everyone deduces from the results written up in the newspapers how they think the mechanics work, and of course they get it wrong because it's profoundly unintuitive.

Re:NYT's Science Going Downhill

[RabidReindeer]

You can't write about quantum mechanics without equations - it is NOT an intuitive field.

The cat wants to know if he can come out of the box now.

Only for easy equations

[Anonymous Coward]

You should insert just easy equations

Definitely

[burisch_research]

Without math, it's impossible to convey what you're trying to convey. The press is way too dumbed down already, and many times I've read science stories that are just plain misleading as they try to simplify the message.

Putting equations into news stories means that some people won't understand them, but most importantly it will encourage some of those people to investigate further, and learn how to read equations. If there's no math in the popular press in the first place, then there's no incentive for people to improve themselves.

Re:Definitely

[cupantae]

I agree with this. What I'd like to see is equations added in, where helpful, in the same way as small images in a body of text. Then you could put a caption below, just to say something informal but informative about the equation. I think that way it would be easy for people to decide whether they want to read it. Some people aren't going to want to, so it's important that it's not something you have to read through in the article itself.

Re:Definitely

[martijn hoekstra]

Without math, it's impossible to convey what you're trying to convey. The press is way too dumbed down already, and many times I've read science stories that are just plain misleading as they try to simplify the message.

Putting equations into news stories means that some people won't understand them, but most importantly it will encourage some of those people to investigate further, and learn how to read equations. If there's no math in the popular press in the first place, then there's no incentive for people to improve themselves.

no equations doesn't mean no math. Equations generally do a pretty poor job in explaining things. I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

Re:Definitely

[Pino Grigio]

Equations generally do a pretty poor job in explaining things. I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

^ This needs a hefty upward mod.

Re:Definitely

[Guy Harris]

no equations doesn't mean no math. Equations generally do a pretty poor job in explaining things.

Yes, they do a poor job in explaining things to people who don't know what the terms in the equation mean; raw math often says little if anything, by itself, about the real world, as you have to connect the mathematical items to items in the real world.

But, BTW:

I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

...I'd rather read an article containing "because, for the same amount of force applied, acceleration is inversely proportional to mass"; my mass is much less than that of a Porsche 911, but I can't even get to 100 km/h on foot or on a bicycle, much less do so as fast as a 911 can. Given equal driving skill and the same driving techniques, however, I could probably get to 100 km/h in a 911 slightly faster than somebody weighing 100kg could in the same 911.

Re:Definitely

[martijn hoekstra]

Yes, they do a poor job in explaining things to people who don't know what the terms in the equation mean; raw math often says little if anything, by itself, about the real world, as you have to connect the mathematical items to items in the real world.

But, BTW:

I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

...I'd rather read an article containing "because, for the same amount of force applied, acceleration is inversely proportional to mass"; my mass is much less than that of a Porsche 911, but I can't even get to 100 km/h on foot or on a bicycle, much less do so as fast as a 911 can. Given equal driving skill and the same driving techniques, however, I could probably get to 100 km/h in a 911 slightly faster than somebody weighing 100kg could in the same 911.

depending on the context that could be a good idea, though an example doesn't immediately come to mind. Completeness may be sacrificed for clarity if there is sufficient context. my above example is obviously a snippet without context, and as such is quite incorrect on it's own, but would also never occur in practice on its own. All context that I can imagine would make it sufficiently clear, especially since nobody would be thinking that acceleration would be a function of mass alone. It's almost like writing articles is a profession that requires more than stringing words together that are correct.

Re:Definitely

[Dr. Spork]

I think that the equation whiners here overestimate the clarity gained when text does include actual equations. I hate to remind you that probably millions of people have stared at the equation with the deltas and the h-bar, and still managed to completely fail to understand quantum uncertainty. In fact, it's a popular view these days that Heisenberg himself did not understand just what his uncertainty results said about the underlying world. And it's not for a lack of seeing the equation. He derived the damned thing.

I also don't think that the author is getting enough credit for just how good a job he did in vividly yet accurately describing what was up with the uncertainty principle. A part of his point is that you don't automatically know what's going on in quantum mechanics when you can solve all the problems on your QM exam and get an A in the course. Even (maybe especially) physicists tell themselves sloppy stories when they think about conjugate properties - I won't say "observables", though that's what we called them in my QM courses. Then when the physicists try to dumb down their already sloppy interpretations for a lay audience, you're on the high road to atrocities like "What the Bleep".

Re:Definitely

[thegarbz]

some people won't understand them, but most importantly it will encourage some of those people to investigate further,

Erm you do know the structure of articles and the state of the readership at large means that "investigate further" in some rare intelligent circumstances where the reader is particularly keen to explore further knowledge, rarely if ever extends to reading to the end of the article.

I don't think anyone at all will read an article and then start on a quest to understand equations within them unless the article is in some obscure field related magazine to the person's work, or they will be graded on their understanding.

Re:Definitely

[cbope]

...but most importantly it will encourage some of those people to investigate further, and learn how to read equations.

Wow, I must live on a different planet. In my opinion, all this will do is make Joe Sixpack say "this ain't important enough for me to learn math, is American Idol on?"

Re:Definitely

[Anonymous Coward]

You completly miss the point. Both are necessary. Both are do a pretty poor job in explaining/describing things taken alone. An article anly containing textual form is weak because the language is ambiguous. An article without description of the formulae is weak beacause you need to be able to interpret as a human being.

Both is unambiguous, linked to reality and interpetable.

http://dilbert.com/dyn/str_strip/000000000/00000000/0000000/100000/40000/7000/700/147746/147746.strip.gif

Re:Definitely

[internerdj]

Math is the example you are looking for; where sufficient education has led to the understanding of how to parse a formula and what the terms mean. At that point we can take the mathematical shorthand instead of the description because the audience is presumed to have all the context from previous interaction. Rule of writing #1 say everything your audience needs to understand it and no more. To the original question, equations are shorthand for understanding very complex concepts. Since most readers lack this context and many lack the skills to even understand mathematical language in a general consumption publication then they should be avoided unless absolutely critical. If you do, then you will likely waste your word count explaining in detail what the equation means and probably undoing the need for listing the equation and possibly alienating readers.

Re:Definitely

[internerdj]

Equations don't do a poor job explaining things. Equations do an excellent job of explaining things...if you have the proper skill to parse them and the educational context to apply them. The problem with using an equation in pop press is that you have to educate the public in the stuff educational context and if you have to go into that detail then you've most likely overridden the benefit of the shorthand mathematical notation.

Re:Definitely

[Anonymous Coward]

The problem with equations is that they often contain some not-so-standard letters that are meant to represent certain concepts. The letter c, for example, is used for the speed of light in a vacuum. So far, so good. But it is also used for capacitance, valve flow coefficients, and to represent some unknown linear constant in a differential equation. What about i? Is it an imaginary number? Is it an electrical current? Is it an index?

The snobs who post equations for the public just assume you know what they're talking about from the context. Most people, however, probably are not as familiar with that context, and so it looks like an impenetrable effort to look like a super-smart jackass.

In reality, it is not the equation that befuddles most people. It is the variables in the equation and what they actually represent. If you explain that, then even someone with only a meager high school algebra background can get a pretty good idea of what is going on.

I'm all FOR posting equations in news stories. That said, I believe that unless we make a special effort to document and discuss every variable in the equation; that publishing such equations will simply confuse people.

Re:Definitely

[Anonymous Coward]

I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

Is there an exclusion principle preventing both from being present simultaneously? The best option would be: the equation, a box of links explaining what each non-trivial symbol means (the majority of readers know addition, division, multiplication and subtraction, but many may have never encountered summation, integration, etc. They're not hard to grasp, but are rather difficult to google. Same with constants, which mean different things depending on the field the equation has come from), and in words what relevance this equation has to the article.

Re:Definitely

[Anonymous Coward]

I may be an odd duck (queue "you're on /." jokes), but if I am reading something interesting and I come across a topic/phrase/word that I'm not familiar with, I will probably just stop right where I am and go look up that new word. Sure, it may derail the original train of thought, but in general it's easy to get back on board by going back a sentence or two.

That said, I agree with the description versus formula, but I would go further to say that including some reference or other parenthetical to point people to deeper understanding would be great, just like Absolute Geek said above.

"... because acceleration is inversely proportional to mass (See Force for more detail)."

Re:Definitely

[NotSanguine]

Without math, it's impossible to convey what you're trying to convey. The press is way too dumbed down already, and many times I've read science stories that are just plain misleading as they try to simplify the message.

Putting equations into news stories means that some people won't understand them, but most importantly it will encourage some of those people to investigate further, and learn how to read equations. If there's no math in the popular press in the first place, then there's no incentive for people to improve themselves.

Exactly. So what if everyone doesn't get the equations? As long as there is some explanatory context around them, that should be plenty. And some folks might even decide (as mentioned above) to investigate and learn something new.

Mathematics is the only way to accurately describe the universe and everything in it. As such, *everyone* should have a keen interest. Heinlein was a bit tongue-in-cheek, but I think he had it mostly right:
Anyone who cannot cope with mathematics is not fully human. At best, he is a tolerable subhuman who has learned to wear his shoes, bathe, and not make messes in the house.” --Robert A. Heinlein

Re:Definitely

[NotSanguine]

I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

Why do you imagine those have to be mutually exclusive? Explaining that "acceleration is inversely proportional to mass" and then using F=ma with a concrete example would demonstrate the concept much more clearly, no?

Re:Definitely

[fleeped]

There's a counterpoint to that. When the relationships get a bit more complicated ( inversely proportional to the square of the log in the power of the absolute whatever that was), the linear and verbose form of text is not as helpful as a neat equation. You can 'read' it with your eyes multiple times really quickly to absorb all the relationships and see the bigger picture of what the formula says.

Re:Definitely

[Savione]

no equations doesn't mean no math. Equations generally do a pretty poor job in explaining things. I'd much rather read an article containing "because acceleration is inversely proportional to mass" than one containing "because F=ma"

That's interesting, I would much rather read "the black body specific intensity is given by B_lambda (T) = (2 h c^2 / lambda^5) / [exp(hc / (lambda * kT)) - 1], where lambda is the wavelength, T is the temperature, c is the speed of light, h is Planck's constant (energy divided by frequency for any particle), kT is the temperature in units of energy, and exp(x) = e^x, than "the black body specific intensity is given by twice Planck's constant times the speed of light squared over the wavelength to the fifth power, all over 1 less than e raised to the Planck's constant times C over the wavelength thermal energy power. There's a reason formulas are the language of mathematics and physics. They are concise, easy to parse, and unambiguous. Contrary to your example, it is easy to see scaling relations without having to add the words for what type of proportionality it is (again, there is a symbol for proportionality that lets you write a simple, easy to understand formula for it). Moreover, you can easily manipulate formulas to show something new. Not so with sentences.

Re:Definitely

[martijn hoekstra]

I would argue that very few to no popular articles need the exact formula for black body specific intensity. But if they do, the formulaic form is clearly superior. It's likelier that the article would focus on a specific aspect off blackbody radiation. To wit, I would expect the majority to talk about the ultraviolet catastrophe, and I wouldn't explain it in terms of equations at all, neither in symbolic nor in written out form.

Re:Definitely

[Darinbob]

The press is too dumbed down to handle almost everything, including politics, war, sports, and starlets.

Re:Definitely

[SoftwareArtist]

If someone can't understand "a=F/m" (or "acceleration=force/mass"), do you really think they have any idea what "acceleration is inversely proportional to mass" means?

Re:Definitely

[martijn hoekstra]

If someone can't understand "a=F/m" (or "acceleration=force/mass"), do you really think they have any idea what "acceleration is inversely proportional to mass" means?

Yes. But that's not really to the point. The point is, that equations break the flow of prose, and don't work well in explaining things, other than in a purely mathematical context. If you are not speaking about mathematics (and nobody other than mathematicians really do, and the OP is rather math related, but is not about the math of the uncertainty principle but its applications) it's best to keep equations out of it. This is obviously a rule of thumb and there are bound to be exceptions where using an equation is actually beneficial to the global understanding of the issue, but these cases are rare, and far in between. For the OP for example, I agree that not using equations was probably the right choice, though I would have made different editorial choices in the prose, and possibly using one equation (to wit, \sigma_{x}\sigma_{p} \geq \frac{\hbar}{2} ) could maybe have been defensible, but still a choice I would have disagreed with.

Re:Definitely

[SoftwareArtist]

Could you justify why you think it's a good rule of thumb? Saying that equations "break the flow of prose" is a purely subjective, aesthetic judgement. Many people would disagree. Saying they "don't work well in explaining things" is objectively false, at least when the thing you're trying to explain is intrinsically mathematical. Writing whole paragraphs of vague, confusing prose to imprecisely describe something that could have been precisely stated with a simple equation is a very bad way of explaining things.

I'm not suggesting equations should be used gratuitously when discussing non-mathematical subjects. But math is fundamental to a lot of things that get discussed all the time in the popular press: finance, economics, public opinion surveys, medical experiments, fuel efficiency, and so on.

Re:Definitely

[John Allsup]

I am reading Heisenberg's Physical Principles of the Quantum Theory and the 'observer effects change on the observed' interpretation is rife.  More modern people tend to use the fact from Fourier/wavelet theory relating how increased containment in the time domain equates to decreased containment in the frequency domain (I like Mallat's book for an explanation of this rather than the QM textbooks.)

Re:Definitely

[originalTMAN]

This is interesting. can you reccomend a book or two with one of these types explanations? Thank you.

No

[Anonymous Coward]

The first article linked is a fairly good layman's explanation. It doesn't need to delve into maths. It explains it better than you did in your comment.

In contrast, your comment has an ungrammatical first sentence, fails to explain the terms well at all, and leaves the reader scratching his head even if he knows the maths already. "the sums of all of the uncertainties - or differences - in a huge pile of measurements of the position and velocity of some particle we're measuring" - what the hell does that mean to a layperson? Now you need to define what the hell all those words and concepts mean, and you reintroduced measurement when the original article took pains to point out it's not about measurement. This is a classic "explanation that only makes sense to someone who already understands it".

Also, your use of 'x' as multiply is entirely non-standard at this level, but hey.

Professional Journalism 1, Rtbinc 0

A better question

[korbulon]

Should articles be written with intelligence and nuance when writing for a "general audience"?

Re:A better question

[Anonymous Coward]

Should articles be written with intelligence and nuance when writing for a "general audience"?

Yes

Yes, please assume high school math

[Anonymous Coward]

But they should start with adding footnotes with references first. Most popular science articles don't even mention their sources properly, which sometimes makes it really hard to follow up on them even if you are a scientist.

Mathematics is taught in schools...

[gweihir]

Everybody not willing to understand simple mathematics (with explanations) is being willfully ignorant. There is no way to reach such people, they would not comprehend the text either...

Re:Mathematics is taught in schools...

[Pino Grigio]

There are many ways to be clever. Understanding math is just one of them. There are many people I know who are engineers, very good at math, but who's writing is terrible (I don't mean handwriting, I mean use of language in written form).

Re:Mathematics is taught in schools...

[Anonymous Coward]

No. Mathematics is absolutely NOT taught in schools AT ALL:
A Mathematician's Lament -- by Paul Lockhart

Re:Mathematics is taught in schools...

[Anonymous Coward]

Whose.

Re:Mathematics is taught in schools...

[dywolf]

Willfully ignorant? Not really, no. People have different aptitudes. And there is a far cry between the math taught in schools to the average person, and the math needed to understand Heisenburg and quantum theory.

Re:Mathematics is taught in schools...

[Anonymous Coward]

Even I spotted that one, and english is my third language, and I'm an engineer ( not super good at math, but still ). Maybe it was intentional?

Re:Mathematics is taught in schools...

[Pino Grigio]

There's no edit button.

Re:Mathematics is taught in schools...

[Anonymous Coward]

There are many people I know who are engineers, very good at math, but who's writing is terrible

That means they are poor engineers. Competent engineering requires the ability to communicate effectively.

Re:Mathematics is taught in schools...

[Anne_Nonymous]

<3
<3
<3
<3
<3

Re:Mathematics is taught in schools...

[Pino Grigio]

Competent engineering requires the ability to communicate effectively

They do communicate effectively, verbally and can get their thoughts down on paper. They just won't be winning the Booker any time soon.

Re:Mathematics is taught in schools...

[Anonymous Coward]

*They're.

Trust me. I have a mathematics degree.

Re:Mathematics is taught in schools...

[Frequency Domain]

So if some author wrote an article discussing finer interpretations of the Bible, citing sections as quotes in the original Latin, Hebrew, or ancient Greek, and you couldn't understand them, that would be willful ignorance on your part?

Re:Mathematics is taught in schools...

[Anonymous Coward]

Regardless of aptitude, you passed high school math.

Which includes algebra.

You can handle equations.

Re:Mathematics is taught in schools...

[Anonymous Coward]

Everybody not willing to understand simple mathematics (with explanations) is being willfully ignorant. There is no way to reach such people, they would not comprehend the text either...

Everybody? Or Anybody? See the problem with language (vs. equations)

Re:Mathematics is taught in schools...

[i]

Everybody not willing to know latin names of plants (with explanations) is being willfully ignorant.

Re:Mathematics is taught in schools...

[zildgulf]

We on Slashdot usually have a good handle on math and we think equations are better because we can condense an explanation down to a few words and a few equations and get on with life. Most of the public does not have a good handle on math, so they are not being willfully ignorant, so words explaining it works better even though it can create long unwieldy sentences.

Re:Mathematics is taught in schools...

[Anonymous Coward]

That just means one can look for patterns and memorize procedures; in other words, it shows that someone has a brain, not that they understand the material.

Re:Mathematics is taught in schools...

[Nethemas the Great]

Minor detail, but the Bible was never written in Latin. Translated, sure but the original languages were Aramaic, Greek and Hebrew. As for understanding, you're missing the "not willing" part. For the moderately educated or better target audience of the NYT it should be of little consequence to reference a dictionary or other reference text should the reader be interested in understanding. In the same way, high-school level mathematics shouldn't be much of a reach. I don't think anyone was suggesting tensor products, or differential equations.

Re:Mathematics is taught in schools...

[Immerman]

An excellent read, I'd mod you up if I had the points.

Re:Mathematics is taught in schools...

[gweihir]

That is why I said "_simple_ math". If you do not understand simple mat, then you are not an educated person. An engineer needs to be able to understand non-simple math. And yes, there are many engineers that cannot write worth a damn. I do not classify them as "educated persons" either.

Minimal requirements in order to qualify as educated:
- Writing to a level that you get your meaning across without causing pain in the reader
- Understanding texts that are reasonably well written and describing things of medium complexity
- Fluent enough in on foreign language that you can think in it
- Basic science understanding, when explanations are given
- Basic math understanding, when explanations are given

Miss one of these, and you are not capable to understand how the world works. That makes you a child, possibly in an adult body. And, yes, I realize that many people that though of themselves as "modern" and "educated" do not qualify.

Re:Mathematics is taught in schools...

[gweihir]

That is "Heisenberg". And no, _basic_ math does not include quantum theory. Which, incidentally, is not math but physics.

Re:Mathematics is taught in schools...

[gweihir]

Requiring one live, widely spoken language as a criteria for an "educated" person is certainly reasonably. Requiring 3 dead ones that are useful for one specific and esoteric purpose is just stupid. Besides that, "finer interpretations of the Bible" is not accessible to the average smart person either, because exegesis is basically mental masturbation requiring a very specific fetish.

Re:Mathematics is taught in schools...

[gweihir]

Indeed. And I said "with explanations" very clearly.

Re:Mathematics is taught in schools...

[gweihir]

And another one does not get it. Math is universal and fundamental to the world, Latin is a specialist skill of limited use.

Re:Mathematics is taught in schools...

[gweihir]

Words are not. You limit yourself to a very low degree of complexity combined with a high level of fuzziness if you limit yourself to words. That means a lot of things cannot actually be explained with words alone. Sure, you can _convince_ people with words, but not based on understanding, but based on other mechanisms.

Re:Mathematics is taught in schools...

[professionalfurryele]

So what metric are you using to claim they are writing poorly?

Arbitrary rules about how writing should be structured are just one more reason much of English is a waste of time. If they don't do the psychology experiment to show that some particular rule of the English language facilitates communication then I have no motivation to obey it.

I will try (and generally fail) to obey the rules because I don't know which ones make communication more effective, if all I have is the witchdoctor then to the witchdoctor I will go. That said sanctimonious English majors can fuck right off if they want to lecture me without actual science backing up their judgemental attitude.

Re:Mathematics is taught in schools...

[Anonymous Coward]

Isn't the Heisenberg equation one of the simplest ones? Even simpler than Einstein's famous one. I don't think we are debating if newspapers should print out PDEs here - I seriously doubt the NY times is even typeset with TeX...

Re:Mathematics is taught in schools...

[Darinbob]

And so people who are great at math and poor at writing should be banished from society and not allowed to work.

Re:Mathematics is taught in schools...

[cheekyjohnson]

Miss one of these, and you are not capable to understand how the world works.

Since many of those are ambiguous, I'd say that's not a very good metric to use. You're not capable of understanding how the world works because I said so.

Re:Mathematics is taught in schools...

[John Allsup]

I don't believe there is any formal measurable definition of mental maturity, so ambiguity is unavoidable.

Re:Mathematics is taught in schools...

[Pino Grigio]

I'm not sure why you're taking it so personally. Nobody's good at everything.

Re:Mathematics is taught in schools...

[cheekyjohnson]

Then I don't think he should state it as if it's a fact.

Re:Mathematics is taught in schools...

[professionalfurryele]

You clearly misunderstood. I don't consider myself bad at something for which there is no acceptable standard.

Re:Mathematics is taught in schools...

[Anonymous Coward]

Where is this far cry, exactly?

Re:Mathematics is taught in schools...

[maxwell demon]

You limit yourself to a very low degree of complexity combined with a high level of fuzziness if you limit yourself to words.

Only if you don't master the language. A text has exactly as much complexity and as much fuzziness as you allow it to have, not less, not more.

If you think a text cannot have a high degree of complexity, however you define that complexity (you didn't give a definition; that's a fuzziness on your part, but that fuzziness is certainly not caused by the use words, but only by your decision to not define it more precisely — or, more likely, your lack of decision to do so), you obviously have not yet encountered any truly complex text. Of course in principle there exists the possibility that you are hyperintelligent and therefore consider even the most complex text as simple, but then you would surely have seen that a text does in no way have to be fuzzy (which by the way again is a term which you didn't really define).

Oh, and you can also put mathematical formulas into words (and when doing so, you can even replace the one-letter names of the quantities by the actual names of those quantities). For example Einstein's famous equation E=mc^2 can be written in words as "the energy equals the mass times the square of the speed of light in vacuum." Of course, the essence of this equation can be formulated as "mass and energy are equivalent." Which has no obvious formulation in equations.

Re:Mathematics is taught in schools...

[Anonymous Coward]

I think your fluency requirement on foreign languages is quite arbitrary -- it's fairly common worldwide to have that skill but not particularly necessary to understanding how the world works. I could just as easily say "learn a foreign language that is not in the same family as your primary language to the level where you can express ideas of moderate complexity with some concerted effort". That's both more and less difficult and gives the speaker both more and less context. I think neither are required.

Also I think your first point is too general. Some meanings are inherently complex and difficult to get across. It needs some context.

Re:Mathematics is taught in schools...

[Anonymous Coward]

He didn't misunderstand at all. It's entirely possible to be objectively bad at something even if there isn't a clear algorithm for how to be good at it. Again, this isn't meant as an insult. And from what I see here, I don't think you write poorly, but this is a small sample space.

Writing is a form of communication. Being good at communication means that you transmit ideas to their intended recipients easily and accurately, while minimizing difficulty/effort/unpleasantness in the reader (and, ideally, maximizing the reader's pleasure/fulfillment/whatever). That's your standard.

If A and B both try to communicate something, and you take large random samplings of people and give them A, and other large random samplings of people and give them B, you can test against each other for results. That's an experimental method.

Take a third random sampling, and have them read both (maybe take a fourth random sampling and present A and B in the opposite order to avoid ordering bias) and ask which one better communicates the ideas. I predict that the answers closely align to the above. I suspect this still holds if the random samplings are now of people who specialize in English writing, though some specific numbers may change.

No, I don't have the study handy to back this up at the moment. This is the experiment that will back up the idea that people in general can evaluate the quality of somebody's writing -- generally an uncontroversial statement. Having established that, guidelines (much more common than "rules") for effective writing can be established by people who specialize in the field on the weight of their own experience.

All this said, I haven't seen a lot of evidence that people who are good at science and/or math are poor at writing. What I do see is evidence that scientific understanding has been poorly communicated for a while particularly with quantum mechanics, and I have a strong suspicion that we could do much better because QM is weird but these concepts are not actually all that difficult. So an obvious hypothesis is that people who understand QM sufficiently are unusually poor writers. Another similar one is that they are unusually disinterested in writing effectively -- frankly, your disdain for English ("English is a waste of time", "to the witchdoctor I will go", "sanctimonious English majors can fuck right off") is a piece of (admittedly anecdotal) evidence in that direction. Another is that QM is inherently difficult to convey. Another is that effective communication is happening, but it is drowned out by a greater population of effective communicators with poor understanding of QM. Another is that effective writing is happening at all levels (eg. expert-to-expert, expert-to-trainee, expert-to-lay-audience) but the audience is not reading the correct writings, and is instead reading things meant for a different audience and therefore taking the wrong conclusions.

Myself, I have a strong suspicion that people who are good at math and science are actually better than average at writing non-science, but get mixed up by simultaneously over-estimating and under-estimating the lay public's competence in the fields of their expertise. I also have a suspicion that QM's well has been poisoned a bit by an accident of history that leaves it at a local minima of poor explanation. I don't think the very most basic groundwork, eg. Heisenberg's uncertainty principle, is really more complicated than things like time dilation which doesn't get nearly as screwed up by the public. It gets screwed up to be sure, but not like this. I just think the public got stuck in some stupid ideas and it'll take something really profound to move the public over the hump into a better understanding, whereas the public landed closer to the mark with Einstein's theories.

Sure, people still refuse to believe that light speed is really a real limit vastly different from the speed of sound, but that's equivalent to people believing that the Uncertainty Principle is just a technical problem to overcome and not fundamental -- it's not equivalent to people thinking the Uncertainty Principle proves souls exist or other such claptrap.

Re:Mathematics is taught in schools...

[professionalfurryele]

I clearly haven't communicated my point very well. I hold formal instruction in the rules of English in disdain, not effective communication. I'm well aware of how you would check what effective communication is, there are even a small number of studies (done by people in Communication Sciences rather than the English faculty) which are very helpful in this regard. They follow exactly the experimental paradigm you suggest.

"This is the experiment that will back up the idea that people in general can evaluate the quality of somebody's writing -- generally an uncontroversial statement. Having established that, guidelines (much more common than "rules") for effective writing can be established by people who specialize in the field on the weight of their own experience."

No, this experiment wont back this up. It will back up whatever rule or guideline was being tested (say 'use a small number of words on a presentation slide') and only if the metric of quality applies. There is no such thing as /*the*/ quality of somebody's writing in general so there is no way to judge it. You can judge my writing by how well I communicate my ideas because I have told you I am explicitly interested in and trying to convey ideas, but it is not a general property. Sometimes we value writing for its obtuseness. Art which conveys layers of meaning subtly for example. To judge my writing style in such a way that I care you need to know my intent (a fact which flies directly in the face of the ever popular New Criticism and other post modernist bullshit which permeates the English academy).

You judge writing style in couple of ways, you can relay your experience, which is fine but only matters if I care about communicating to you in particular, or you can relate my writing style to some generalisable epistemology. The only one of those we have is the scientific method. English does not use the scientific method, as far as I can tell it uses no effective epistemology what-so-ever. If anything those who study English (rather than communication) are more disinterested in effective communication than most scientists.

I never said I was disinterested in effective communication. I said English majors and people who adhere to rules about how writing should be done can fuck off. While the statistics and experimental methods of communication science might be a bit dodgy at times I have nothing but respect for that endeavour and have used the fruits of that particular scientific process to improve my own writing and presentation.

The rest of your post I largely agree with. You outline a collection of nuances and particulars which would impact a careful, scientific study of science communication. Something which people who complain about how I end this sentence would have trouble getting at. People who study English are doing a bad job because they think there is an objectively correct way to write. They are doing such a bad job I just praised Communication Science as a discipline in comparison.

Re:Mathematics is taught in schools...

[gweihir]

Only if you don't master the language. A text has exactly as much complexity and as much fuzziness as you allow it to have, not less, not more.

Sorry, but wrong. Encoding does matter when you process information. Mathematical formalism was invented exactly because conventional language is largely unsuitable to be used as a basis to describe mathematical ideas. While in an information-theoretic sense, you can misuse conventional language to describe things you can state with mathematical formalism, it becomes difficult to achieve exactness, and the memory foot print becomes much, much larger, readability is down, etc. The result is that people that could understand the formalism cannot understand the natural language. It just does not fit into short-term memory anymore and it is cumbersome enough to handle as to be unusable. Mathematical problems need to be stated clearly, and, as important, compactly in order to be understandable. Of course, you need natural language initially, to explain the elements of the formalism, but describing even not that advanced mathematical things only in natural language fails. It has been tried in the past, read some of the mathematical texts from people that did not have suitable formalism at their disposal. Unless you are genius-level, the only way to do it is by formalizing what they are saying. And even on genius level, natural language becomes the limiting factor of what you can understand because of non-compactness, linearity, fuzziness and other problems.

You are falling for the same fallacy as people that claim COBOL is self-documenting and the code is "natural language" after all. That is not the problem in understanding it, as mathematical symbolism is not the problem in understanding mathematical statements. The symbolism actually makes it a lot easier and often possible in the first place to understand it.

Another example is Roman numerals: There is strong indication, the number system the Romans used severely limited what they could do in engineering and commerce, as it was hard to read and did not deal well with large numbers. And yes, numbers as used today (g-adic notation based Arabic numerals) _is_ mathematical formalism. Try writing out some numbers and you should immediately see how unsuitable normal language is to state mathematical ideas. The Romans did not fail to see they needed formalism to state numbers, they just invented a bad formalism that came with severe limitations.

Re:Mathematics is taught in schools...

[maxwell demon]

It has been tried in the past, read some of the mathematical texts from people that did not have suitable formalism at their disposal.

Older mathematical texts are hard to read because the mathematicians lacked the abstractions we have today. For example, the statement "the vectors form an orthonormal basis" is a very complex statement if you don't have the vector space abstraction. It's complicated both when written in formulas and when written in text. Basically you have to state explicitly that there's no non-trivial linear combination which gives zero, and you have to state that for every single component (but without being aware that those are components of vectors, and therefore not being able to use that fact in the formula or text). That's definitely not pretty. As soon as you know the concept of a vector space, it's the simple statement I've given above (and BTW, I wouldn't know an equally simple formula expressing the same fact).

Also I never claimed that formulas don't have an advantage when actually doing or seriously using mathematics. However it is not true that language is necessarily inexact or fuzzy. It generally takes more words to say the same thing. But then, it's easier to remove irrelevant details without getting wrong. Note that removing irrelevant details is not fuzziness or inexactness, but conciseness. Anyway, you lost the context: We are not speaking about mathematical texts communicating mathematical content to other mathematicians, we are talking about journalistic texts communicating to non-mathematicians essentially non-mathematical content which happens to contain some applications of mathematics.

You are falling for the same fallacy as people that claim COBOL is self-documenting and the code is "natural language" after all.

You are comparing apples and oranges here. But then, I hope you don't claim that it is impossible to create well-written programs in COBOL. Which would be the closest analogy to your claim that replacing mathematical formulas with natural language inevitably gets fuzzy and inexact.

Re:Mathematics is taught in schools...

[gweihir]

There is one way to keep natural language descriptions of mathematics non-fuzzy: Transcribe the symbolic notation. That is incredible stupid and it does harm clarity. Any other way and you end up being fuzzy. There is no way around that and it is well-known to mathematicians. For example, informal proofs are only accepted by mathematicians, because the reader is expected to have to skill to create a formal one form the informal proof.

And no, I do not believe I lost the context at all. Texts targeted at non-experts can do two things: 1) Take the readers for idiots and abstract so much away that they basically have to believe whatever the claim is, as the text does not explain why anymore or 2) actually explain the claim in a verifiable fashion.

A Brief History of Time would suggest that

[auric_dude]

"The author notes that an editor warned him that for every equation in the book the readership would be halved, hence it includes only a single equation: E = mc2. Early in 1983, Hawking approached Simon Mitton, the editor in charge of astronomy books at Cambridge University Press, with his ideas for a popular book on cosmology. Mitton was doubtful about all the equations in the draft manuscript, which he felt would put off the buyers in airport bookshops that Hawking wished to reach. It was with some difficulty that he persuaded Hawking to drop all but one equation.[4] In addition to Hawking's notable abstention from presenting equations, the book also simplifies matters by means of illustrations throughout the text, depicting complex models and diagrams." https://en.wikipedia.org/wiki/A_Brief_History_of_Time it may not be true as after all the book sold rather well.

Re:A Brief History of Time would suggest that

[Anonymous Coward]

it may not be true as after all the book sold rather well.

But how many of the people who bought it truly understood? Probably only an elite few.

Re:A Brief History of Time would suggest that

[dcollins]

This is what I came here to say, too. The "no-equations" dictum is pretty much an ironclad rule from editors and publishers. The author in question basically has no say in the matter. Which is pretty messed up, in that everyone is required to take basic algebra to communicate in that language, and then it's banned by fiat from our popular media.

Re:A Brief History of Time would suggest that

[Anonymous Coward]

This is what I came here to say, too. The "no-equations" dictum is pretty much an ironclad rule from editors and publishers. The author in question basically has no say in the matter. Which is pretty messed up, in that everyone is required to take basic algebra to communicate in that language, and then it's banned by fiat from our popular media.

Really ?

So why did publishers actually publish Roger Penrose's

The Emperor' New Mind (it has a chapter on lambda-calculus and introduction to quantum theory)
The Shadows of the Mind (it has chapters dealing with logical imcompleteness, quantum theory and spin formalism to quantum gravity)
Roads to Reality (your "learn theoretical physics and then more in 48 hours) kind of book) ?
Wheeler's Spacetime Physics: Introduction to Special Relativity (the popular book not the other one). ?

In fact the best popular science books are those that use equations to explain concepts. Hawking's books while critically acclaimed are actually almost devoid of any interesting substance. They have been sucked dry. Precisely because there is no equation to be seen and metaphoirs can only carry you so far.

Re:A Brief History of Time would suggest that

[SoftwareArtist]

If equations (even very simple ones) were more common in the popular press, then people wouldn't be so afraid of them, and editors wouldn't feel the need to remove all equations even from books on very mathematical subjects.

Depends on the audience

[Anonymous Coward]

Seeing the average education of the general American public, no. Maybe if you wrapped it in some "new" math...? Surely this time that'll work!

You missed the point.

[Anonymous Coward]

Maths is just a metaphorical language that even fewer understand.

Equations as PR

[Sockatume]

Come to think of it, if the tendency for PR firms to arrange for an "equation for the best sandwich" etc. suggests that an equation is actually quite an easy way of getting the public's attention.

Re:Equations as PR

[gutnor]

That's because those equation are "funny". It is tongue in cheek for people school days "when they understood all that stuff"

If the equation look real enough, people will just zone out, or worse, assume that the author opinion must be true since there is a formula.

Re:Equations as PR

[cheekyjohnson]

It is tongue in cheek for people school days "when they understood all that stuff"

So... probably never, then.

A good start

[rossdee]

They should start by using proper units. I know the USA is not metric, so they can use feet, miles and pounds, but football fields, states of delaware and volkswagens are not proper units. (and especially Library of Comgresses)

Re:A good start

[ratbag]

Personally I think that part of the problem is the non-metric units that are still in use. By accepting that it is in any way sensible to use them, you've already given up on the logical, elegant approach to quantification. You've made it more likely that people resort to the "football fields" etc.

Re:A good start

[Sockatume]

Those aren't units of measurement, they're points of comparison. That's why they're preceded by phrasing like "as big as".

Re:A good start

[dywolf]

as someone who measures for a living, metric isnt some magical entity that cures all ills. all (real) units have some precise definition, held and maintained by a body or agency of standards, and your vast oversimplification of "everyone different than me" is insulting and itself ignorant of the field of measurement. if the conversion between units scares you, i suggest getting a calculator.

Re:A good start

[Anonymous Coward]

Most people don't have an immediate idea of what 5000km or .001 mm mean. Giving them a point of reference gives them a way of wrapping their heads around it.

Re:A good start

[ratbag]

No, not a magic bullet, but a self-consistent, extensible, logical, location-independent basis for straightforward communication. Conversion of units doesn't scare me, it just seems a splendidly archaic and sometimes error-prone way to spend time. A quick trite example: without knowing where your interlocutor lives or works or chooses to base their unit system on, tell me how much liquid is in the gallon container next to my desk?

"Everyone different from me" is amusing, maybe even ironic, though I don't know where you hail from so I can't be sure.

Re:A good start

[ratbag]

To pre-empt any silliness, let's say the container is full of a liquid stable at the local room temperature.

Re:A good start

[Anonymous Coward]

Should I be changing my LoCs to Petawords?

Re:A good start

[Anonymous Coward]

Even in places where metric is used as standard, you have abominations like the "metric ton" written in press. Apparently, picking one system of measure over another doesn't remove the idiot human from the equation.

Re:A good start

[Aviancer]

You're right! Which is why I downloaded a really cool Chrome extension which does neat things like locate numbers in text and provide reference points. To whit:

Most people don't have an immediate idea of what 5000km [~ typical distance covered by the winner of the 24 hours of Le Mans automobile endurance race] or .001 mm [~ also called one micron] mean. Giving them a point of reference gives them a way of wrapping their heads around it.

Re:A good start

[Anonymous Coward]

A gallon, by definition.

Re:A good start

[Immerman]

Obviously it contains 2746 smidgeons. Next question?

Re:A good start

[westlake]

They should start by using proper units. I know the USA is not metric, so they can use feet, miles and pounds, but football fields, states of delaware and volkswagens are not proper units. (and especially Library of Comgresses)

Illustrations drawn from everyday life and experience are easier to understand than the geek's's mathematical abstractions --- and understanding is what matters here, not the geek's sense of propriety,

Re:A good start

[yoghurt]

It's worse than that. They invariably uses the wrong unit for the quantity. Measuring power in Joules or current in Volts or similar nonsense. Every time I see an article with any science in it I cringe in anticipation of the incorrect units and quantities.

In crosswords, I come across the clue "electrical unit" for which the answer is "rel". I am an EE and have no idea WTF a "rel" is.

Re:A good start

[Darinbob]

Precise communication is very important. Thus, because non-SI units are the most commonly accepted units in the US, it is logical to use those units to communicate.

Re:A good start

[Darinbob]

A kilogram is as big as one thousand grams!

Re:A good start

[ratbag]

because non-SI units are the most commonly accepted units in the US, it is logical to use those units to communicate.

And US scientists and engineers never communicate with colleagues, competitors or customers from (most of) the rest of the world who have embraced the future (circa 1795-1975)?

Can you see why a previous comment about "everyone different than me" tickles me?

Re:A good start

[Darinbob]

I have a colleague who thinks Americans are inherently stupid because of not using SI. He extends this to even auto mechanics. He goes nuts over this stuff. He refused to acknowledge that to work and live in the US that you must deal with US measurements.

Yes, if you are a US scientist then you deal with SI units. If you are a US engineer it's half and half, often you must use SI, but at other times you must use local measurements, not all engineering disciplines are identical. All of them deal with miles and feet and pounds when they're not at work, they deal with a speed limit that is expressed in miles per hour, their doctor will tell them to lose a few pounds, they buy gasoline in gallons, etc.

Re:A good start

[maxwell demon]

Units of measurements are points of comparison.

Re:A good start

[maxwell demon]

According to Wikipedia, rel is a Dalek unit of time measurement roughly equal to one second. :-)

Re:A good start

[Anonymous Coward]

Yes, but the implicit assumption that people have a better idea of how much text is stored in the Library of Congress than of how much 10 terabytes are, is a fallacy. I've never been to the Library of Congress and I have no visual idea of how many books there are, but I know by direct experience how many pages of text, hours of audio/video, etc. fit in a terabyte of disk space. I've never been to a football game, but I can picture a rectangle of 100 by 50 meters (= steps, roughly). Why not just use the common units of measurement instead of Libraries of Congress and football fields? I'm sure they are the most intuitive tertia comparationis for most people. And they're certainly more intercultural than all these middle-US-centric pseudo-measurements that remind me of the dark ages of Reader's Digest imperialism.

Re:A good start

[Anonymous Coward]

And you forgot to mention, it's base 10. Our numbers (when we're not talking about bits'n'bytes) are base 10, not base 12, 16, 20, 60, ...

Mental capability

[Taco Cowboy]

Most of those who have studied advanced math have heard of the Heisenberg's Uncertainty Principle, but not every single one of them understand it

Putting the same Heisenberg's Unvertainty Principle to the "average Joe on the street" and you would most probably get a blank stare

This has nothing to do with elitism, this is about reality

Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?

Re:Mental capability

[Anonymous Coward]

Most of those who have studied advanced math have heard of the Heisenberg's Uncertainty Principle, but not every single one of them understand it

Putting the same Heisenberg's Unvertainty Principle to the "average Joe on the street" and you would most probably get a blank stare

This has nothing to do with elitism, this is about reality

Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?

Give me a break. In the 1920s Einstein wrote a popular book about special relativity (with formulas) and general relativity for the layman. And we're talking about 2 theories which at the time were at the frontier of physics research. In the last 90 years we haven't suddenly become idiots, so if popular science books talking about special/general relativity and quantum theory (a theory 90 years old !!!!) don't use equations it is because of stupid preconceptions. I've said it before people are not idiots, they may not be specialists in physics research but you can certainly explain them the basics of 2 theories which are almost 1 century old using carefully selected formulas. Nobody goes apeshit if you write Newton's formula of gravitation, why would you go crazy for Heisenberg's uncertaintly principle ?

Re:Mental capability

[Pino Grigio]

He wrote a book. How many people bought it? How many people read it? How many people understood it? How many people skipped the math?

Re:Mental capability

[RabidReindeer]

Most of those who have studied advanced math have heard of the Heisenberg's Uncertainty Principle, but not every single one of them understand it

Putting the same Heisenberg's Unvertainty Principle to the "average Joe on the street" and you would most probably get a blank stare

This has nothing to do with elitism, this is about reality

Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?

Give me a break. In the 1920s Einstein wrote a popular book about special relativity (with formulas) and general relativity for the layman. And we're talking about 2 theories which at the time were at the frontier of physics research. In the last 90 years we haven't suddenly become idiots, so if popular science books talking about special/general relativity and quantum theory (a theory 90 years old !!!!) don't use equations it is because of stupid preconceptions. I've said it before people are not idiots, they may not be specialists in physics research but you can certainly explain them the basics of 2 theories which are almost 1 century old using carefully selected formulas. Nobody goes apeshit if you write Newton's formula of gravitation, why would you go crazy for Heisenberg's uncertaintly principle ?

The cynic in me observes that in this country, every issue is expected to divide into 2 diametrically-opposed sides. Such as, for example, the party that eats their own babies which is the exact opposite of the party that eats everyone else's babies (yes, those are exact opposites and you can only chose one. Snarf).

Furthermore, in adherence to this post-Einstein Weltanschaung that everything should be as simple as possible, then made simpler, everything must be expressed in short sound-bytes suitable for framing on bumper stickers.

So shouldn't E=mc**2 be short enough? No, because statements like this require context. If you don't know what E, m, and c represent, it's just another math equation. And context won't fit on the bumper sticker.

I've actually had people tell me that no one but Einstein is smart enough to understand Einstein. The Gods themselves...

Re:Mental capability

[Anonymous Coward]

He wrote a book. How many people bought it? How many people read it? How many people understood it? How many people skipped the math?

Considering it has been in print ever since, I'd say it sold and continues to sell pretty well.

Re:Mental capability

[Maelwryth]

"Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?"

Are you suggesting that we hide maths entirely? Look, there are some things I maybe understand a little, many things I don't understand, and probably an infinite amount of things I don't know about. Just because I don't understand something doesn't mean you should hide the problem from me. If maths is the best way to understand something then it should be used. If an article refers to data or a paper then it should be referenced. If you hide things from me (lies to children?) then I have to repeat the work of others to come to the same result. That is called a waste of time.

You, and I, (if you and I exist) are in a situation where the supposed greatest minds of our race understand maybe 2% of the rules. Probably far less. Although it is far more comfortable to sit in frount of media, dealing in made up social structures, assuming that what I can see is real, pretending I know it all and living in a fantasy land. I would quite like to have an inkling of what I don't know. It makes me humble, and it makes me careful.

The map is not the terrain. The rules are not the reality. Shine me a torch to see. And if it is dark, tell me of the possibilty of light.

Re:Mental capability

[Anonymous Coward]

the fucking article starts with numb3rs reference.

connecting quantum mechanics as reason for someone having common sense is bullshit and math has nothing at all to do with it.

Re:Mental capability

[Anonymous Coward]

>why 1 + 1 = 2, and not 1 + 1 = 3 ?

Actually people know "1+1=2" as a fact and never question it and what it really means. i.e. the formal proof behind it.
We did proofs like that in logic class and they were at least half a page long.

Re:Mental capability

[cheekyjohnson]

To certain groups of people. I also doubt that many people truly understood it.

Re:Mental capability

[Anonymous Coward]

The fact is, special relativity is something a person could wrap their minds around with equations accessible to a general audience. That would be good. Not it was not done with general relativity, which (in most cases) requires much more difficult math to demonstrate anything interest. And only the very very simplest dumbed down to the bottom of the barrel of quantum mechanical things are as mathematically simple. So do it with special relativity (if there is any need to in the news), or start with some classical mechanics that is newsworthy, but that case does not generalize.

Re:Mental capability

[serviscope_minor]

Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2

I work with integers modulo 2, you insensitive clod!

Re:Mental capability

[Pino Grigio]

Indeed. It's also interesting to note that Einstein's original papers are eminently readable to the Layman, compared to the kind of papers we see in journals today. Perhaps that's due to the complexity of the mathematics now advanced at the bleeding edge, or perhaps it's because journals try to be even more economical with space than they used to be. I don't know.

Re:Mental capability

[Pino Grigio]

+1 for making good use of the word Weltanschaung.

Re:Mental capability

[Anonymous Coward]

You want a general public discussion about the definition of the word "three", or about Peano's axioms? I'm not sure what the point of that is... we figured it out already, mathematicians moved on a long time ago, and everyone else never cared.

Re:Mental capability

[Pino Grigio]

Nothing is hidden from you. You have Google. When I wanted to understand what Yang-Mills theory was, I went to Wikipedia. Finding that impossible to understand without knowing what a Gauge Theory was I hit another link. This continued on for some time and now I'm Rouse Ball Professor of Mathematics at Cambridge University.

Re:Mental capability

[malkavian]

But some learned wondrous things. And used that to go even deeper. Isn't that what education and learning is all about?
If it appeals to enough groups to stay in print, that's a fair number.;

Re:Mental capability

[Anonymous Coward]

Perhaps that's due to the complexity of the mathematics now advanced at the bleeding edge, or perhaps it's because journals try to be even more economical with space than they used to be. I don't know.

I would attribute it to common circlejerking among mathematicians.
Many 'modern' mathematicians tend to use more archaic or complex notation for the sake of showing off even in cases where it doesn't reduce space or make it more readable.

Heck, even if you just look at the wikipedia articles for math subjects you see this trend. Rarer notation are often used over one that could be understood by the layman. Hardly suitable for an encyclopedia but the writer had a desire to show off rather than to educate.

Re:Mental capability

[Anonymous Coward]

Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?

Most mathematicians don't even understand the meaning of =, you can hardly criticize average Joe for not comprehending 1 + 1 = 2 when those who work in the field skips the philosophy it is based on.

Re:Mental capability

[sycodon]

In the last 90 years we haven't suddenly become idiots

Umm...Look around you.

Re:Mental capability

[datavirtue]

No, it's elitist, insecure academics playing nick-knack on your brain to cover up their own lack of knowledge and insecurity. Try hanging out with academics--90% are severely insecure and defensive. Remember the BOFH who uses tech speak to smash down users?

Re:Mental capability

[datavirtue]

If I were to stand outside the universe and observe it then 1+1=2 would prove to be false being that matter is equal to energy. Therefore there is no two of anything--if you really want to be pedantic. It is only a *fact* in our current context of observation.

Re:Mental capability

[Talderas]

But I want to be in the party that eats any baby.

Re:Mental capability

[Anonymous Coward]

Indeed. It's also interesting to note that Einstein's original papers are eminently readable to the Layman, compared to the kind of papers we see in journals today. Perhaps that's due to the complexity of the mathematics now advanced at the bleeding edge, or perhaps it's because journals try to be even more economical with space than they used to be. I don't know.

Be careful, they seem readable but they're full of subtilities (and in some places even contain errors) especially his 1905 article on the Electrodynamics of Moving Bodies.

And furthermore while they "are" readable to today's audiences because we have almost a century dealing with special relativistic phenomena (it has even entered popular culture) it was not so at the time.
Take that into account.

Re:Mental capability

[Anonymous Coward]

You damn ECC guys...

Re:Mental capability

[Anonymous Coward]

How many people need to apply the math contained therein in their everyday life?

Hint : It`s closer to "0" than it is to "everyone"

Re:Mental capability

[Anonymous Coward]

No, 1+1=2 has absolutely nothing to do with observation (other than that the concept of numbers originally was invented to capture the observed behaviour of things). Numbers are abstract concepts which stand for themselves and are independent of anything you may or may not observe. Even if we find out that there's no physically existing thing which exactly corresponds to the numbers, the numbers still obey the same laws. For example, I'm pretty sure that we will never find anything in the universe with the cardinality aleph_omega, but that doesn't change any mathematical insights we have about that cardinality.

Re:Mental capability

[Anonymous Coward]

No, he's right: It wasn't a sudden event.

Re:Mental capability

[RabidReindeer]

But I want to be in the party that eats any baby.

doubleplusungood. There are only TWO parties. They are 100% opposite of each other. There can be nothing else. There is nothing in between. There is no outside position.

You are obviously mentally deranged. Stay where you are. MiniLuv will be along for you shortly.

Re:Mental capability

[Anonymous Coward]

Actually, most people understand 1+1=2. It is basic counting! The few that doesn't, aren't reading newspapers either.

Sure, they should use more math in the papers. The journalists might have to learn LaTeX though, might be hard on them.

Math in the newspapers wouldn't scare people away. Not even hard math. Anybody can find lots of things in a newspaper already, that they don't get or have no interest for. Some hate ads, some hate foreign news, some hate sports, and so on. Math would be just another thing that some like and some doesn't like. But if you're writing about a topic where math comes up naturally - use it. Lots of everyday math is no more complicated than y=ax+b anyway, simple formulas that lots of people can understand. Not all of course, but we don't aim every newspaper article at everybody. Some doesn't know what 'Angola' is either . . .

Re:Mental capability

[Darinbob]

After the revolution, the moderates like you will be first against the wall.

Re:Mental capability

[Darinbob]

It was a long sequence of people standing on the shoulders of the midgets who came before them. Honey Boo Boo could not appear on the Discovery channel until society was ready for it.

Re:Mental capability

[Talderas]

I'm an equal opportunity consumer. I HAVE NO SHAME.

Re:Mental capability

[jfengel]

The paper on special relativity is fairly readable. The general relativity paper is practically illegible to the layman, requiring tensor mathematics that are usually not taught until the later stages of a physics degree.

He did, however, try to make it more generally accessible, at least to the determined student. This paper is pretty amazing:

http://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity

Re:Mental capability

[maxwell demon]

But -1 for misspelling "Weltanschauung".

Re:Mental capability

[Pino Grigio]

Copy/paste gets me every time.

Re:Mental capability

[MiSaunaSnob]

Idiot 1 + 1 == 10

Re:Mental capability

[Anonymous Coward]

Or perhaps he was just better at writing than most researchers today?

Remember that peer-review is both a curse and a blessing. You get the people who mostly know what you know, mostly live the same life you live (Publish or perish! Publish or perish! Publish or perish! Cthulhu! Cthulhu! Cthulhu!), and think the way you think. Somebody else with an advanced degree in the same field will almost certainly have trouble reading the majority of papers in the field they have their degree in but which are on topics outside their specialization, but your "peers" don't need or want things spelled out, and they're the one's who approve or disapprove the paper.

Having many researchers in a field writing in a foreign and not-well understood language also tends to reduce the quality of the overall writing in that field. Such low quality writing quickly becomes accepted as the norm.

Actually taking the time to become good at writing is largely irrelevant to success in such circles, even counter-productive. It's also bad for job security: making the bar for entry as high as possible is standard operating procedure for many people these days. It's not just the legal profession that is riddled with ethics problems.

No.

[DeathToBill]

Equations are a great way of explaining something to someone who is familiar with equations. Someone who has done first year undergraduate maths and done reasonably well at it will appreciate having an equation to explain something.

Someone who did fairly poorly at high school maths will look at an equation and say, "What???"

Take Newton's second law. You can explain it in two ways. The first:

When a force is applied to a body, it accelerates in proportion to the force and inverse proportion to its mass.

The second:

F = m a
F = force
m = mass
a = acceleration

To someone familiar with mathematical models, the second is intuitive; if you increase the force, the acceleration increases. If you increase the mass but keep the force constant, the acceleration will have to decrease to satisfy the equation. But you have to already have that intuitive grasp of what an equation means, or the first explanation is always going to be easier to handle.

Re: No.

[Anonymous Coward]

Perhaps stating that F is the cause and a is the effect would make things a bit clearer. Write an equation but state what it is.

Re:No.

[Anonymous Coward]

I disagree with your example. If you can't glean that relationship in the equation you are highly unlikely to understand what an inverse proportional relationship is. However, it can be explained in simpler terms; i.e. "if force remains the same, a smaller mass will have a higher rate of acceleration. The faster rate being proportional to the difference in mass."

Re:No.

[Anonymous Coward]

Yes, but what exactly is Force? mass? acceleration? (and in turn, what exactly is speed and time? what is position?). Sure you can write an equation that make them all relate to each other, but that's still about as intuitive and descriptive as X = Y*Z. If you don't believe me, try figuring out the intuition behind E=mc^2.

Re:No.

[Anonymous Coward]

Yes, but what exactly is Force? mass? acceleration? (and in turn, what exactly is speed and time? what is position?)

Force: That what allows the Jedi to move things around with their mind.
Mass: A Christian religious event performed by a priest.
Acceleration: A payment ahead of the original schedule.
Speed: A drug.
Time: A magazine.
Position: A political statement about some topic.

SCNR :-)

Re:No.

[Anonymous Coward]

The equation

F = ma

tells you more than the sentence. First it tells you that the force varies *linearly* with mass and inverse *linearly* with acceleration. Double the mass get exactly double the force. The sentence version implies this, but does not lock you down on that issue.

Also, the equation gives you an explicit way to measure force, which the sentence does not. It even tells you what the units might look like ( kg * m/(sec^2) ).

Would Dr. Callendar have been better off

[Anonymous Coward]

Would Dr. Callendar have been better off just diving in and dealing with Heisenberg

Maybe, but I can't wait to see how Hank Schrader is going to deal with Heisenberg.

Re:Would Dr. Callendar have been better off

[Chrisq]

Would Dr. Callendar have been better off just diving in and dealing with Heisenberg

Maybe, but I can't wait to see how Hank Schrader is going to deal with Heisenberg.

Also if he was diving wouldn't that mean that his position on this wouldn't be clear?

Most Ph.D. don't read mathematics

[jarek]

I've written lots of reports with math formulas (in Latex) where they are needed. Most, if not all, the intended readers have a Ph.D. in experimental physics or optics but I noticed that unless the math is really trivial, they will not follow. Even the slightest math supported reasoning will throw them off. That experience tells me that math for the general audience is probably not a good idea. It is simply pointless the be correct if you are not coming across. Who hears the tree falling in the forest.

Re:Most Ph.D. don't read mathematics

[stenvar]

You need the explanation to understand what the paper is about. You need the formulas to verify your understanding and to verify the work.

Many people don't read your formulas because they don't have to: they want to get the big ideas, but they aren't interested in verifying your work. For example, your result may be simple enough that they can verify it themselves, or they may decide that it isn't important enough to bother verifying it.

But for your scientific work to be complete, the formulas (or other formalisms) still need to be there, even if most people never look at them.

Re:Most Ph.D. don't read mathematics

[marauder]

This is oddly reassuring. I'm a reasonably smart guy, a strong statistician and programmer, and I cannot follow formulas. They're not intuitive and I have to painstakingly work through and translate them as if they were a foreign alphabet. I sometimes wonder whether that's just me, but it seems not. I note that someone in TFA's comments posted a mathematical explanation to demonstrate how much clearer it made things, and at the first Greek letter I skipped to the next comment. No doubt everyone in the 'general audience' would do just the same.

Re:Most Ph.D. don't read mathematics

[Anonymous Coward]

If you have written many reports, but most of your intended readers have not understood them, perhaps the problem is not their comprehension.

Re:Most Ph.D. don't read mathematics

[dinfinity]

You need the formulas to verify your understanding and to verify the work.

I think that indicates that a lot of people would like to understand the equations, but that they just consider it too much effort.

The thing with a lot of equations is that they are too concise to be easy to understand. I'm going to make a programming analogy here: Looking at any sufficiently sizable and advanced formula is like looking at a sufficiently sizable and advanced regular expression. Sure, if you take the time to carefully examine the regular expression, you will find out what it matches for. It will take a lot more time, however, compared to the exact same regular expression split up into functionally named parts.

An example:
pattern = "\b(25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\.(25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\.(25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\.(25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\b"

compared to:
matchUpTo255 = "25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\.(25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?"
pattern = "\b("+matchUpTo255+")\.("+matchUpTo255+")\.("+matchUpTo255+")\.("+matchUpTo255+")\b"

The latter is obviously much simpler to understand, in part due to using a variable name that has meaning to a human. I'm not saying that using a similar approach for all equations is going to be an option or even desirable (simplifications could be overlooked), but when it comes to making them easily understandable to a broad audience: I'd rather see more of it!

Re:Most Ph.D. don't read mathematics

[Anonymous Coward]

That's one part of the story, but another part is that the formulae often don't actually tell you all that much. (My background: theoretical physics.) Without the surrounding text you often cannot even tell what the formula is about, let alone if it's correct, and if you have read the surrounding text then the formula is almost superfluous and only of interest if you are e.g. going to reimplement a model. (In the exact same way the author did, because often I find it easier to take the ideas and apply them to the new situation.)
Observation: If a text contains formulae, scientists read the text but skip the formulae. But laymen skip the text; if you want to make absolutely sure that your text isn't read by anyone who doesn't have a degree in the exact sciences, put a formula in there somewhere. It doesn't really matter how trivial it is.

Re:Most Ph.D. don't read mathematics

[Trepidity]

For me this depends on the area. In many parts of CS, you can safely ignore the equations, because they end up being needlessly tedious formalizations of something that was already said in two sentences, and proofs of trivial properties by structural induction. I guess there's a certain "nice to be sure" aspect of restating even straightfoward things with symbols, but rather than having them in the paper, in those cases I'd rather their proofs be formalized in Coq or Isabelle or something and included a checkable appendix. Proofs of obvious properties that are verbose and formal, but not actually formally checkable, occupy a sort of worst-of-both-worlds no-man's land.

Re:Most Ph.D. don't read mathematics

[stenvar]

Well, as someone who does a lot of math and programming, I understand what you mean. But in most formulas, remembering the variable names really is a small part of understanding the formula. When there are problems with formulas, they are usually poor organization, poor abstractions, or errors.

Re:Most Ph.D. don't read mathematics

[dinfinity]

I guess your code also only contains single-letter variables? Because it has absolutely no effect on readability or ease of understanding? You just 'remember' what the variables are? Especially when you're looking at somebody else's single-letter variable code?

Tell me, what's easier to understand for a layperson:
F = ma
or:
force = mass * acceleration

It's really very simple. Rewrite any equation as a high level programming language expression, using (lots of) sensible variable names, and the equation becomes instantly more understandable for pretty much anyone.

Look at the page for the Heisenberg Uncertainty Principle: http://en.wikipedia.org/wiki/Uncertainty_principle
The first equation you see is completely meaningless to the uninitiated.

Lets rewrite it:
positionStandardDeviation * momentumStandardDeviation >= REDUCED_PLANCK_CONSTANT / 2

Not only is it a lot easier to understand for people who understand what a standard deviation is, you'll also remember it much easier.
Unless you don't speak English.

Re:Most Ph.D. don't read mathematics

[stenvar]

force = mass * acceleration

It's really very simple. Rewrite any equation as a high level programming language expression, using (lots of) sensible variable names, and the equation becomes instantly more understandable for pretty much anyone.

Unfortunately, that's not really "understanding". You really only understand the equation if you actually understand what force, mass, and acceleration are. Once you know that, you generally don't have any trouble remembering the variable names.

Re:Most Ph.D. don't read mathematics

[dinfinity]

1. I never said that people would somehow magically understand all equations. I said it would make them more understandable.

2. Actually, the equation in this case is (of course) equivalent to x = y * z. The meaning of the variables is what makes the equation interesting in the first place. And somehow you are arguing that using the word representing the meaning of a variable is pretty much identical to using an arbitrary almost ungoogleable single-letter symbolic representation of it when it comes to understanding what an equation using said variable means?

3. The problem is not 'remembering variable names'. The problem is finding out what the fuck they mean in the first place. Do you really believe that the average Joe when confronted with math in his (online) newspaper will be able to 'remember' what the symbol for standard deviation was? No, because if he's ever seen it at all, it was probably in a context where his mind wasn't really soaking up the knowledge, so to speak.

Re:Most Ph.D. don't read mathematics

[stenvar]

Do you really believe that the average Joe when confronted with math in his (online) newspaper will be able to 'remember' what the symbol for standard deviation was?

No, I think the average Joe won't be able to understand formulas at all, no matter how you present them. If you present them in words, he may think he understands them more, but that will be a false sense of understanding.

Re:Most Ph.D. don't read mathematics

[dinfinity]

No, I think the average Joe won't be able to understand formulas at all

That is the dumbest thing I've ever heard.

You haven't talked to a lot of average Joes, have you? I've tutored some, and the two things holding back understanding are disdain for the subject among their peers and elitist assholes that approach them with condescension. Think about that the next time you curse at the people for not grasping basic statistics, voting like sheep or uttering stupidities.

Also, thank you for conceding to my other points.

Re:Most Ph.D. don't read mathematics

[Anonymous Coward]

The only point I concede is that you have clearly proven that you are a jerk.

general rule

[l3v1]

The general rule regarding the depth of detail in publications should be that they need to be understandable by the target audience. If you write for the general public, then the base text should be layman style, with some pointers where to get more in-depth information for those, who are above the average and more knowledgeable in the specific field. If the target audience is academic and/or scientific community of a specific field, then that's a totally different matter, and the text should be as to-the-point and in-depth as possible, since anyone from the audience would be able to produce superficial treatment of a topic in their field, even if they are not utmost experts of the specific topic, and they'll require exact and deep elaboration of the subject to be able to judge the subtleties, novelties, benefits, etc. I'd say that's all, and it's really not 'rocket science', just spend some time getting to know who'll you'll address with your writing.

Re:general rule

[SoftwareArtist]

This rule is circular. Why doesn't the general public understand equations? Because equations never come up in anything they read. Why don't equations come up in anything they read? Because editors think their audience won't understand them.

The solution is to educate their audience. I don't mean sending everyone off to more years of math classes. I mean just including very simple equations now and then in their articles and explaining what they mean. That's a journalist's job: to educate their readers about things it's important for them to know.

Re:general rule

[maxwell demon]

That's a journalist's job: to educate their readers about things it's important for them to know.

No. The journalist's job is to inform you about what's happening, and provide necessary background information you need to form your own opinion.

Not equations. Graphs.

[goodmanj]

The innumeracy of the public is at a lower level than that. This is like arguing about whether kids should be taught calculus in school when they're struggling with basic arithmetic.

What we need is not more equations in the press, but more graphs, tables, and diagrams. I can't count the number of times I've seen a journalist try to explain, say, changing poll results or the interplay between mortgage rates and foreclosures using text, plus a quote from an expert which they clearly don't understand, when all they need is a quick line chart.

I'm a college professor, and in my classes that require essays I insist that the students incorporate graphical charts, maps, and diagrams. Generally speaking, they're awful at it, but it gets them thinking about data.

Protip

[Anonymous Coward]

You can safetly ignore any sentence that includes the phrase "according to quantum mechanics".
-xkcd

Re:Protip

[Dr. Spork]

In most contexts this is too true, and quite sad. However, if you aren't allowed to tell a story "according to quantum mechanics", you have no chance of explaining the functioning of the ordinary objects all around us, like lasers, LEDs, microwave ovens, fucking magnets, superconductors, sunshine, and many others. The real problem is that "according to quantum mechanics" has been so abused that people reflexively glaze over when they hear it. That abuse has made the world stupider and sadder, and undoing the damage is a valuable endeavor.

Re:Protip

[Anonymous Coward]

Which xkcd?

Science articles are not written for a general aud

[physicsphairy]

Science articles, one would presume, are written for persons interested in science. The idea that there is some broad swath of persons who wish to understand quantum mechanics but stand to be chased off by a simple formula strikes me as unlikely.

If it is a problem, then the logic is the kind of the logic that will perpetuate the problem: the reason math is not as digestible to a public audience is because they're not accustomed to it, and they're not accustomed to it because the media is choosing not to present it to them.

blatherskite

[Anonymous Coward]

Callender's op-ed was great. Quantum physicists are the biggest bullshhitters around.

Re: blatherskite

[Anonymous Coward]

Most of the people doing the theoretical work are just mathematicians. They often use words without regard to their actual meaning. A great example was "imaginary" numbers. Whenever they write or speak in plain language, they don't know what their talking about because they have no clue what words actually mean.

Another good example is the line that "a positron is just an electron moving backward through time" - not if the plain language meaning of time is intended.

Igon Value problem

[Anonymous Coward]

Use equations and references to equations at your own peril if your target audience has any clue of what you're talking about. Just as /. doesn't suffer fools, writers who write about the maths when they don't have a idea what they're talking about risk getting exposed and embarrassed. Pinker did this to Gladwell.

No...

[mendax]

Why reawaken the horrible and traumatic memories of school? Well, unless you were like me who was always good at math. In my case, I would object to news stories containing more references to bullying and teasing. But I've forgiven my childhood bullies of all that. It was easy to do and I've since and I've forgotten most of it. Forgetting it was just as easy as forgetting where I buried their bodies after I took my revenge. *muahahahaha* Ok, I'll take my pills now.

how about this one

[Anonymous Coward]

M = h - c

Re:how about this one

[Chrisq]

M = h - c

I get the point - equations are meaningless without surrounding context

Re:how about this one

[Anonymous Coward]

A perfect illustration of the value of equations. I read the two nyt articles and understood nothing. But then I read your post and now I understand physics.

Re:how about this one

[Anonymous Coward]

(Math, arithmetic) = (hard enough) without (being Chinese)

Re:Nah.

[Anonymous Coward]

The author is a philosopher, not a physicist or mathematician, so he probably doesn't understand the mathematics used in QM anyways.

So why is he writing about QM ?
Why not make Hilary Putnam write articles about the interpretation of QM and therefore about the significance of the Heisenberg uncertainty principle ?

Useless

[Impy the Impiuos Imp]

Absolutely not.

Wikipedia has already fallen prey to this. Articles on all these things are just dense reference manuals iseful only to graduates in their subjects rather than enlightening explanations.

They failed when those same people got full of themselves taking over the subject matter. They are as useless as a "man page" on regular expressions.

Re:Useless

[Anonymous Coward]

Manning got 136. thats not mathematically proportional to what he did.

Re:Useless

[Anonymous Coward]

Just wait until http://simple.wikipedia.org devolves into a million fiefdoms too.

Re:Useless

[Anonymous Coward]

I personally find the man pages on regular expressions to be quite useful, and use them often.

Re:Useless

[Anonymous Coward]

Huh?

Wikipedia has everything. Some pages of dense reference material, but what is wrong with that? Nice when you don't have the textbooks for your field handy. Faster to search than a textbook too!

Wikipedia articles aren't all written to be understood by everybody. Neither are the books in the library - which include textbooks & reference material for every field there is. Still, the library is considered immensely useful.

And then, there is lots of wikipedia articles with no math too. I tend to skip those though.

Diagrams are the way forward.

[Anonymous Coward]

Equations are short hand and full of a form of jargon specific to a field, in terms of the arcane symbols used to represent a property or constant, with the explanation of what each symbol means buried in the text. They are great at condensing meaning, and allowing somebody familiar with them to manipulate them easily. But they are actually terrible at conveying meaning to someone not familiar with the field it is describing.

Often diagrams are the best way to explain mathematical concepts where possible. In the end, most scientist presents with a set of equations or concept to understand, will inevitably spend some time plotting out or trying to pictorially described what it means, to help understand it. So why not short circuit that?

Re:Diagrams are the way forward.

[EE_Nathan]

Yes! As my math/physics teacher always told me in school, "If you can draw the picture, then you can do the problem." Granted, many advanced concepts are harder to draw a picture of than a ladder leaning against a wall to determine the free body diagram, but just look at some of the great work being done at phdcomics to express scientific concepts graphically. A picture is worth a thousand words and maybe at least a dozen equations.

Re:Diagrams are the way forward.

[westlake]

In the end, most scientist presents with a set of equations or concept to understand, will inevitably spend some time plotting out or trying to pictorially described what it means, to help understand it.

The reporter Mark Sullivan ("Our Times," ca. 1930) made good use of imaginatively conceived charts and maps in his pioneering social history of the early twentieth century. The idea caught on as a way of playfully illustrating complex statistical data, political and social analysis.

The United States of Paranoia

Yes

[Anonymous Coward]

Been wanting to see this for a long time.
I am not particularly good with math but I'm sick of programming that targets the lowest denominator.
If the shows people watch are constantly making them feel like morons because they don't understand anything, maybe they'll actually be encouraged to learn something for a change...

Re: Yes

[Anonymous Coward]

But that would make them switch off their television and stop consuming advertising. What self respecting media conglomerate wants to encourage that kind of antisocial behaviour?

Re:Not equations. Graphs.

[livingboy]

I think that graphs are often quite misleading. Especially when they are used to show statistical information. You can make very different graphs from same base data. One chooses the graph trying to get best propaganda value.

That is why we have the phrase "Lies, damned lies, and statistics"

Dumb and Dummer

[AndyCanfield]

My (48-year old Thai) girlfriend starts work at 6am and gets off at 6pm. She insists that means she works thirteen hours a day. It is amazing how incredibly dumb the average person is.

The Internet was invented at CERN to share research data among atomic scientists. Today the biggest use of the Internet seems to be Facebook.

The average IQ is supposed to be 100; until I moved to Thailand I had probably never even MET a person with an IQ below 110. Theory? Equations? Try "Unable to subtract 6am from 6pm". Science has all along been faced with the necessity of publishing conclusions, because the average person cannot comprehend the data or the formulas. Atomic science was ignored until Hiroshima; since then it is observed but rarely undrestood.

Re:Dumb and Dummer

[Anonymous Coward]

Did you just call your girlfriend incredibly dumb?

Re:Dumb and Dummer

[captjc]

I don't know where you lived before moving to Thailand, but I want to go there. Here in the US, I have a difficult time finding people with an IQ over 110. Oh sure, there are colleges and R&D firms with plenty of bright people but step outside and find there is nothing but morons as far as the eye can see.

Re:Dumb and Dummer

[Anonymous Coward]

subtract 6am from 6pm

6pm-6am = 6m(p-a)
That would be six milliprobabilityminusacceleration

Re:Dumb and Dummer

[Anonymous Coward]

Does it take her half an hour each way to work?

Maybe she isn't dumb, maybe you just lack the social skills to listen to full sentences from her.

Re:Dumb and Dummer

[Anonymous Coward]

Did you just call your girlfriend incredibly dumb?

Looks like it. How dumb is it to be with someone you can't respect? What next? Get children you can't respect and blame it on their mother?

Re:Dumb and Dummer

[Anonymous Coward]

theres quite big cultural differences too asians in general can't even draw maps...(their tourist guides wtf)

Re:Dumb and Dummer

[Anonymous Coward]

Why not? If she is? It's ok to call her incredibly beautifull is she is. Or incredibly tall. Or short. Or fat. Or skinny. Might not be ok to call it to her face, specially if she is incredibly unsecure and gets offended.

Re:Dumb and Dummer

[Anonymous Coward]

Why not? If she is? It's ok to call her incredibly beautifull is she is. Or incredibly tall. Or short. Or fat. Or skinny. Might not be ok to call it to her face, specially if she is incredibly unsecure and gets offended.

Why would you be together with someone you would characterize differently behind her back and to her face? What does it even mean to be "together" with someone you talk down in public? What kind of shithead would do that?

Re:Dumb and Dummer

[r2kordmaa]

Working 12h and billing for 13h doesnt seem that dumb to me.

Re:Dumb and Dummer

[Anonymous Coward]

Oh hey there Dunning-Kruger effect ,about time you showed up in this thread.

I have a relevant equation on the topic...

[Bomazi]

...but /. doesn't support math markup.

Re:I have a relevant equation on the topic...

[Anonymous Coward]

Use ASCII-art, you insensitive cod!
of course, :P

in any field

[Anonymous Coward]

what one would tell a layman would seem confusing and over simplified to an expert.
what you would tell an expert would baffle and confuse the layman.

Write for your audience, if you do it right, they may want more information and acquaint themselves with the more advanced versions of it.

More than equations are needed

[MarkWegman]

Graphs are very helpful in really conveying what is going on. What we need more in discussions of politics is facts and many facts are about numbers. When discussing who has the right model of the US economy you really need to think of it scientifically. Each model is a hypothesis that needs to be tested. Economics is about aggregate behavior and so it's really a statistical statement. Yes the models are equations and those are nice to show too. But you need to show graphs. Folks who are not innumerate often prefer for example what Nate Silver put on fivethirtyeight.com to talking heads on TV who use neither equations or graphs. Many folks I know prefer Krugman's blog http://krugman.blogs.nytimes.com/ to what makes it into his columns in the Times.
If you can't show pictures of aggregate behavior you can only tell stories. Those stories can tug at heart strings and motivate people to feel strongly about an issue without really understanding the whole picture. That's one of the problems with our political discourse.

Heisenbergs is used as a metaphor

[Anonymous Coward]

I work as a software developer, and when ever I am trying to find the cause of a crash that appears only when the debugger is NOT attached, I think to myself: "Damn this Heisenberg guy.". And then I giggle.

As long as no one comes up with a better word for the situation, I'll abuse Heisenbergs Uncertainty Principle –and will have fun while doing it.

Here in Germany, we call it "Heisenbergs Unschärferelation" which translates to Heisenbergs unsharpness relation. Which I find more to the point. Now I wonder, why it was not translated to Heisenbergs Mystery Principle, that would have been much more catchy. Inaccurate but catchy

Cheers
-- Benjamin

Advanced math = less equations

[Anonymous Coward]

The more advanced you get in math, the more textual it becomes, so no, don't think more equations are needed. Some visual representations may be better suited (e.g. matrices). I doubt an elliptic curve equation would make anything easier to understand... its graph on the other hand might

Most people in the US have very limited exposure

[mark_reh]

to the name "quantum mechanics" and probably figure that it is a guy who uses a wrench to do something on a car. "Heisenberg" is a guy who cooks blue meth on TV using methyl amine instead of the usual Nazi method.

You want to put math in newspaper articles? That would first require that journalists and editors understand the math. Journalists in the US generally can't differentiate between news and the crap they report on as if it were news (who won on American Idol, etc.).

America, F YA!

[Anonymous Coward]

I prefer to keep America stupid.

Arthur C Clarke

[kramulous]

Didn't Arthur C Clarke have this argument with his publishers? Every equation resulted in a 80% reduction in audience?

Something to that effect.

Re:Arthur C Clarke

[vossman77]

In "Brief History of Time" Stephen Hawking states that "Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, E = mc^2. I hope that this will not scare off half of my potential readers."

http://en.wikiquote.org/wiki/Stephen_Hawking

Re:Arthur C Clarke

[kramulous]

Me ... waaaaaay off.

Thanks.

Absolutely !?

[Anonymous Coward]

Unfortunately our society is taught to fear mathematics. For some odd reason people do not want to go beyond qualitative reasoning, which is insufficient if one wants to really understand physics. I would not shy away from using Mathematics. Put down an equation and explain it in words. How hard can that be? If people don't know what a term means let them look it up. Newspapers should not contribute to enabling a lazy society. (PS: I am a physicist)

Re:Absolutely !?

[John Allsup]

And of course, once you get back to hardcore dynamical systems, qualitative reasoning tends to resurface due to the inability to analytically solve things.

Use graphs

[Anonymous Coward]

Most math articles use graphs to convey math principles. Because equations are hard to read and even harder to interpret right, while most people can understand graphs.

popular science

[Anonymous Coward]

Lets face it, this is what popular science is, science with science taken out of it. To make an academic paper readable(not even understandable) for general public you have to strip it of all context, not just big and scary numbers and equations. Trying to explain advanced physics to layman is futile effort in the first place. Whats the point to even try to explain quantum mechanics to an average person who doesn't even understand Newton's laws of motion?

Solution is simple.

[Anonymous Coward]

Certain articles should have a warning on them, like a health warning, that the article is "Not for thickies".

Entropy

[Anonymous Coward]

In my experience, the concept of entropy gets abused a hell of a lot more than the Heisenburg uncertainty principle.

Re:Entropy

[MiSaunaSnob]

was entropy acting on you when you wrote this random statement? All threads should be random if you really think about it

Use pictures

[Richard Kirk]

I do not think the original article was a success for various reasons. It is not easy to explain quantum mechanics convincingly, and I don't think the lack of equations was a main weakness. Those of us who are happy with equations with Hamiltonian operators and eigensolutions probably understand the uncertainty principle too. Those of us who have not touched serious maths, or have done it too long ago will be made to feel stupid rather than being helped.

I think what the article needs was good pictures. How about...

A picture of the Young's slit experiment. A light wave goes through two slits, and interferes with itself. You get fringe patterns. You can calculate the fringe patterns using classical physics.

A picture of the Stern-Gerlach experiment. An electron beam is split into two and interferes with itself. You get similar fringe patterns. What, what? This works with electrons? Yes, it even works with substantial molecules such as buckyballs. In fact, if you did your Young's Slit experiment with a very dim light source and a long integration time, you would be passing photons, one at a time, through the apparatus.

So, when a particle interferes with itself, does it go through the left slit or the right one? Some people say it goes through both, but it doesn't, really. The wave function, which we can calculate but we can't measure, may go through both slits in some senses, and determine the fringe pattern. If we install a detector that can tell us the electron is going through the left slit, or going through the right slit, then the electron goes through one slit, and we do not get the interference pattern. We can know which slit the electron goes through, or we can predict the interference pattern, but we can't do both.

A picture of a wave packet plotted in ordinary space, and in frequency space.

There is nothing magical about the observation, itself. The idea that being observed changes the states dates back to an old and rather unhelpful thing called the Copenhagen model. A better approach is to say that we can measure some property of a particle wavefunction such as the position, or the momentum of the particle; but in measuring the position we lose the ability to also measure the momentum, and vice-versa. In this case, the width of the wave packet determines how accurately we know where the particle is at the time of measurement, while the width in frequency space determines how accurately we know the momentum. Our measurement will tell us what the wavefunction was like at the point of the experiment, but nothing else. This is one form of the Uncertainty principle, but it can be applied to other measurements too.

See, it can be done. If you don't get it, don't worry: small things and quantum stuff are pretty weird.

To a degree, yes

[sirwired]

Most literate people could probably handle arithmetic, fractions, simple exponents, some basic geometry, and linear equations.

However, I would not expect a general-audience article to feature calculus, statistics (beyond references to the mean and median), complex algebra, differentials, etc. As in, everything past pre-algebra class is sketchy, at best.

But algebra beyond linear equations, any kind of complex geometry (beyond rote formulas), calculus, just about anything with a sigma symbol in it, etc. I'm a Computer Engineer, and I don't remember how to do any of that stuff. Format of an equation describing a parabola? Method for computing integrals? How to calculate Standard Deviation? I've forgotten it all; it was 15+ years ago, and has no relevance to my day-to-day life. I could probably pick it up again relatively quickly if I needed to (okay, except for calculus and linear/diffEq; I sucked at it even at the time), but yeah, my eyes would start glazing over any article that relied on my understanding of even moderately complex math.

Re:To a degree, yes

[Anonymous Coward]

Writing for a general audience generally targets 6th or 7th grade reading level. Seems like a similar rule would be appropriate for math, which probably leaves algebra and geometry right out.

Re:To a degree, yes

[Anonymous Coward]

I give you that diffeqs and integrals are hard, but "anything with a sigma symbol in it"? A big sigma is just a loop that sums up some expression over an index variable. As a programmer you should be familiar with that. When the steps get smaller and smaller, the sum morphs into an integral, and those are indeed hard to grasp with a discrete (= programmer's) mindset.

Dullards Don't Read

[Anonymous Coward]

At least dullards are not prone to delving into anything about physics. So an article about the uncertainty principal might benefit from a bit of math.. However for almost all other articles mathematics will tend to make even more occult the subject at hand.

I think the OP was on the wrong track

[sirwired]

I read the OP's letter, and while it was a great explanation of the actual details of the uncertainty principle by going over what the different variables meant, it didn't enhance my understanding at all. (Not least of all because it left out units.)

It stated the principle, and gave it's exact formula, but didn't tell me why it was true; it said it just was, and that was final. The NYTimes article explained WHY you can't measure both location and velocity simultaneously, and how this does and does not have application in our day-to-day world. The detail that minimum uncertainty is confined to the value of the Plank constant (especially when no units are given) is utterly irrelevant to somebody reading a general-interest science article.

Yes.

[Karmashock]

Because if he doesn't cite the math not even the people that know the subject will know if he's right or wrong.

A big problem with "expert opinion" in the press is that they never have to substaniate their opinions. They instead make very vague arguments and say they would get into it further but not in the laypress. Then they fail to follow that up with any further publication in the specialized expert press where all readers could be assumed to understand the subject.

That needs to stop. Either cite your opinion with enough information to know whether your argument is false... OR don't do it.

Re:Yes.

[i]

Shouldn't "people that know the subject" know if he's right or wrong without equations from his side ?

Re:Yes.

[Karmashock]

No. Because simply being familiar with the subject or understanding it does not mean you understand his argument which might be new.

no and yes

[Anonymous Coward]

if you explain the principal in a understandable way FIRST, then you can go about going *tada*:"and as a equation it looks like this!"
NOT the other way around. trying to explain an equation is futile.
also i would like to raise an objection:"we are NOT measuring in physics. we are COMPARING!" google translates the german:"verhaeltnis" as english:"relation".
"verhaeltnise studieren" "study relationships". yes? no? maybe?

Start with the logic first

[umafuckit]

Equations are just a way of expressing logic. Well thought through and logically written science articles aren't particularly common in the mainstream media, with their love scare stories, etc. I think a vital first step would be to improve on the quality of the in general articles and guide the reader through the scientific process. Once they've nailed that (if they every do) the presence or otherwise of equations is hardly worth worrying about.

Re:Not equations. Graphs.

[marauder]

If someone has an axe to grind, it's easy to make graphs lie. Lying with inferential statistics is a bit more involved, so that gets held off until third year. (No joke, I had a research methods assignment that required me to formulate conclusions then generate a dataset to support them.) But when you legitimately want to understand what's in data, or explain it honestly to someone else, the right visualisation beats statistics every time. Humans are pattern detectors, graphs contain patterns, statistics are just numbers. If you can't see a finding in the visualisation, and you have to rely on a statistical test to demonstrate it, there's a high risk that it's not really there.

That article

[argStyopa]

The problem with the original article was that the writer asserted effect for cause:
"....Why exactly is the uncertainty principle so misused? No doubt our sensationalist and mystery-mongering culture is partly responsible. ..."

No, we have a sensationalist and mystery-mongering culture for the same reason we have superstition: fundamental human ignorance, and a failure of the educational system.

It's part of (I believe) a basic function of the human brain to try to organize and explain the environment around them. Lacking a known understanding, this drops to the default state of 'make shit up that reasonably fits the observations'.

Of course, whether one 'gets' the uncertainty principle may or may not be considered fundamental science education; I'd rather argue not. Nevertheless, the point is that with a firm grounding in basic sciences, EXPLAINING the uncertainty principle should be reasonably possible.

To the point of the poster, I don't believe 'equations' would have really made a difference in the presentation. I agree with the article's author that "measurement" is not intrinsic to the uncertainty principle, and in a sense it confuses it by getting 'down in the weeds'.

In my experience - and I'm hardly science-illiterate - equations 'lock in' relationships and are absolutely necessary for understanding, but equations are rarely useful in EXPLAINING something in general principles. In the same sense: explaining a game is usually is easier than throwing a rulebook at someone and telling them to "figure it out"

I knew a very good programmer...

[Anonymous Coward]

...who was terrified of basic linear algebra. I'm talking first order, single variable equations. This guy wrote data acquisition software and ran his own MUD for years. I told him once, "It's no different than a variable in a program." He shrugged and shook his head. So did I.

Do you?

[Anonymous Coward]

Most people simply do not have the mental capacity to comprehend the meaning of 1 + 1 = 2, and if you do not believe me, go ask the people around you, why 1 + 1 = 2, and not 1 + 1 = 3 ?

Uncertainty is studied in philosophy. There is nothing in mathematics that will help you understand why 1 + 1 is always 2 except that 'my teacher told me so'.

Fact is, there is nothing stopping 1 and 1 becoming three tomorrow, or even in the next moment. The only thing we have to go on is the perception that it has always worked in the past. That is no guarantee of the future. Should you chose to follow the probabilistic approach to reasoning in this question your chosen approach also falls into the same problem that has been uncovered. Essentially it is one of those inconsistent cases where math cannot give you the answer while more pure (but less precise) logic systems can.

It is easy to see what an apple divided into no parts is; it is still an apple. Yet dividing a number by zero does not give any answer at all. Likewise it is not difficult to see that, should 1+1=2 for the entire history of the concept, even though there is nothing showing that it may be the same tomorrow, it would be foolish not to assume that it will continue to do so.

Re:Do you?

[Immerman]

Indeed - addition was the foundation of mathematics and was established as a general solution to the a priori knowledge gained from counting - I count pile A as having 3 things and pile B having 5 things, and if I count them together I always get 8 things. Eventually we abstracted that knowledge away from the particular things we were counting, and later came up with shorthand notation for long repetitive sequences of addition (multiplication and exponents), but that knowledge comes from the basis of mathematics as a model for the physical universe, not from any sort of provable theory. Okay, there are proofs that 1+1=2, but they're typically either comedic exercises in circular reasoning or part of a proof that Axiom Set B is a superset of Axiom Set A (which along with proof that A is a superset of B will prove that your alternate set of seemingly ridiculous axioms is logically equivalent to one of the broadly accepted sets)

Your apple example is fundamentally flawed though - you can't separate an apple into zero parts - it starts as one part and that number can only increase as you divide it. To separate it into zero parts you would have to remove everything *else* in the cosmos so that the apple is no longer a thing separate from cosmos but instead defines it, which is about as close to infinity as you're going to get.

It's pathetic

[HalfFlat]

We don't expect journalists to write articles only in Basic English. If someone were to profess that they had never heard of Shakespeare, or didn't know what a metaphor was, we would rightly judge them as being ignorant, or at the least, highly under-educated. Yet, apparently, balking at the simplest of equations is perfectly acceptable.

It's no wonder that we have such shallow thinking, such an abysmal and superficial political discourse, such a disengagement with the notions of science and society, when everyone is given a free pass when it comes to mathematics and logic. Put equations in your writing. Judge those who complain about 'math'. People who are unwilling to think can barely be counted as citizens, having abrogated a fundamental and necessary duty.

Regular ignorance can be cured. Wilful ignorance is a blight. We need to demand better of our peers.

Re:It's pathetic

[Anonymous Coward]

Umm, because we use English every day? From email, to talking to the cashier, co-worker, boss, and friends. We don't just use English as a system, but we live in such system.

I value math and I find formulas to be really elegant and amazing. I honestly think it's poetic. However, me and most people don't talk in math formulas. We might live in it, but we certainly don't notice it. My car's automatic transmissions and fuel timing is completely....well, automatic. The cashier either just scans the bar code or types in the code. Even simple algebra is not used anymore. The only time I have to use math is when I go to restaurants and calculate tip percentage. On the other hand, I use English to talk to the waiter, and even write this post. The NYT is a general information publication, not an academic journal. Those two have very different audiences. I don't expect NYT to explain what postmodernism is either, but only inform me of what the art gallery/ museum show will feature, who curated it, and the time of the opening. I tend to skip the "review" because I want facts, not opinions.

I could make the very same arguments you make about the US law and constitution, and deride those who don't partake in city council meetings. Go ahead, replace all instances of 'math' and 'equations' for law. It's easy to judge, especially when you don't know the world around you.

Here's a conundrum

[Anonymous Coward]

Is anyone entirely certain that NYT's typesetting system is capable of producing mathematical formulae?

Things to make you go "hmm..."

Fuck the morons

[Anonymous Coward]

Just matter-of-factly belt out the math, don;t get a boner over it just present it, and move on. If they can't understand it too fucking bad.

Not in pieces on "New Age Philosophy"

[Anonymous Coward]

Having read the article, I don't believe in using equations in articles on "New Age Philosophy"

I believe a big red graphic across these articles with "This is utter drivel written by idiots for idiots" would be far more appropriate.

No maths needed

[jandersen]

The author struggled to make clear his point and left the impression he was creating a strawman argument

Strange - I found his arguments (in the first article, didn't read the second) quite straight forward, and I feel that adding equations would only have obfuscated matters. Most people don't understand equations and inequalities or their specific significance, and that goes for a lot of well-educated people too. The significance of Heisenberg's inequality is that you can use it in quantitative calculations when you test your theory, but it does not in itself add much to your intuitive understanding of the principle.

The problem with the article IMO, is that the subject really does require a reasonably strong background in experimental physics. You need to know something about how experiments in particle physics are conducted, how the results are calculated, etc, before his arguments fall into place.

Statistics

[Anonymous Coward]

Journalist have a propensity to throw statistics at your face without anything to back them. It's totally misleading
and sometimes (quite often) they make mistakes in their interpretations.

In the case of Statistics, I think journalist should give more informations and maybe explain how to interpret the statistics.

Math in the news.

[HybridST]

More equations would certainly be a good thing but the general populous simply doesn't understand them. There's a quote from Hawking concerning 'A Brief History of Time':
"Someone told me that each equation I included in the book would halve the sales. I therefore
resolved not to have any equations at all. In the
end, however, I did put in one equation, Einstein's famous equation E=mc^2. I hope that this will not scare off half of my potential readers."

My suggestion for online publication is to include Starship Troopers style "would you like to know more" links as sidebars seldom work on phone-level hardware. In a print article you could include an 'in depth' url.

Histograms

[Anonymous Coward]

It would surely make me more comfortable to see a graph instead of all those fantastic averages!

no.

[Anonymous Coward]

By the tone of your post, you seem to imply that the press is idiotic, catering to the idiotic masses. I'd argue that they're trying to be understood, which unfortunately requires "dumbing down" information. I wouldn't understand anything a pharmacy professor would say about organic chemistry if he showed equations. But I can understand metaphors in the English language. The purpose of the press is to inform, not to educate. If you want an education, there's always Khan Academy.

Magazines, on the other hand, might approach your goals of educating the crowd a bit closer. If I saw the Quantum article on Popular Science or the Smithsonian magazine, I'd be tempted to learn more. With newspapers, I just digest it and move on to local and national politics, and then living section. I only read newspapers in the morning to stay informed, and move on to the next newspaper. I want facts, not opinions while having breakfast. I read analysis at the end of the week when hopefully all facts are gathered. I can't stand speculation, especially with hour-by-hour newsbreaks inaccuracies (i.e. Spanish train derailment; mass shootings).

As for the equations, the author should stay with the lowest-common denominator: the English language. It's not a perfect system, but it is one adopted by most people rather than the math formula language where only a relatively few understand it.

Absolutely

[Mr.CRC]

The first time I saw some advanced mathematical equations, I said "what the f*ck is that jibberish?" I knew at least that it was a type of math I never saw before, and quickly became obsessed to find out what it was. I proceeded to copy a whole bunch of it onto my notebook cover. My Vo-Tech Electronics instructor informed me that it was "calculus," and gave me an introductory text. After struggling a bit to get it, I finally began to understand derivatives, and proceeded to obsessively hand differentiate pages and pages of expressions the hard way, by taking the limit after algebraically manipulating the expression substituted into the fundamental definition of derivative. Then I proceeded to work through all the standard derivative form proofs. This was while being a stoner, and coming darn near dropping out of high school. Finally, my maturity caught up to my inherent potential after age 21, and I was able to succeed at college after the 3rd try, and land a respectable career as first a Chemist, then a Laser-Optical Technologist, then finally an Electronics Engineer.

The ability to learn calculus on my own planted a crucial seed of confidence in a person who had little self-esteem. This seed would later blossom into a strong autodidactic tendency which was a major factor in helping me get my act together.

Point being, you can never predict what will inspire people to discover something good about themselves which may ultimately lead to a contribution to society. So it is better to just let them have the truth.

Also, ignorance is not knowing that you don't know. At least if they are shown the equations, they will realize that they don't know what the heck it means. If that disturbs the egos of 0.0001% into wanting to learn something, then that is good.

Finally, raising a child has taught me that people behave according to the expectations placed on them. Within the constraints of their inherent ability, of course. But even that is somewhat plastic! I'm convinced a large element of our societal troubles stems from attempting to absolve people of responsibility for themselves.

There is a choice

[gr8_phk]

1) You use no math. This conveys no information to those who might actually take something away from an article, while giving the masses a fluff piece which at best make them think they know something about the topic.

2) You use math. Now you can convey something meaningful to some part of the audience. You'll turn off some people too, but at least they'll realize they don't actually understand it.

One is better for sales, Two is better for humanity.

E=mc^2

[qualico]

A good book to read on this topic is David Bodanis's E=mc^2,
"A biography of the world's most famous equation"

It's not just another Einstein book. It's actually about just the equation and its life.
The author gives examples of how printing houses using different equation notation were like Microsoft, driving out the competition for the standard.
All manner of symbols were used for math, some examples:

e================== mc^2
e || mc^2
e -----------> mc^2
e .aequs. mc^2
e ][ mc^2

Anyway, yes equations "can" be nice too look at in mainstream media.
Only to show a simple proof or to inspire a reader into further learning.
Of course, if it looks like spaghetti to the masses, then maybe the publisher went too far :P

Regardless, wasn't Einstein known for explaining complex concepts in terms that even the non-scholastic could understand?
Don't think he used any equations to describe relativity to them.
In fact, Einstein was not even a good Mathematician, iirc.

Re:Science articles are not written for a general

[Trepidity]

Many people not particularly interested in science have some passing interest in what scientists have found, which is what the popular press is often going for. Less "how does quantum mechanics work?" and more "how did humans evolve?", "does [X] give me cancer?" and "what is anthropogenic global warming?".

"Beginner's" Calculus

[Dareth]

An introduction to Calculus from an MIT video series.

The first video requires so much previous knowledge to follow. The average person would have no idea what they were saying. And this is "Introductory" to the basics for what is being discussed in the article.

Re:"Beginner's" Calculus

[r2kordmaa]

If you have a uni degree, of any kind, you should easily understand all of it(lot of it are really high school topics). If you don't, something must be wrong with your degree, check if the warranty is still valid.

Re:"Beginner's" Calculus

[readingaccount]

There's always someone who has to bring someone down rather than consider their point might have some merit.

Re:"Beginner's" Calculus

[Anonymous Coward]

If the point is that many people really don't learn much even if they are throat fed the knowledge, then yeah, parent post has lots of merit.

But what would he know?

[Minwee]

"Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, E = mc^2. I hope that this will not scare off half of my potential readers."

-- Stephen Hawking, "A Brief History of Time"

and more

[Anonymous Coward]

Maps and graphs too.

What about Porn magazines?

[sageres]

Can we do something like "Holy shift! Look at that asymptote on that mother function!"

I avoid pop-sci books with such

[peter303]

Its kept me from buying Penros's "Road to Reality" and Susskind's newest pop physics books. And I have a PhD in a physical science.
The exceptions seem to be books about mathematical philosophy or tricks.

Math is a language

[Frontier Owner]

Math is a language of its own. putting the equation in an article is fine as long as its something that would be understood. We use words from other languages all the time in English,

rather incomplete book

[peter303]

First, Einstein wrote a larger equation in his original 1905 paper including a momentum term.

Second, the derivation of the equation is as fascinating as the what the equation implies. It is derived computing energry with Lorentz contractions. Only high school algebra and physics needed - no calculus. But adding very deep physics intuition which eluded two centuries of previous mathematical physicists. The intution is that holding the universe to a speed limit says rest mass equals energy.

Re:rather incomplete book

[qualico]

Interesting, that there was a larger equation,do you have a link for that?
Have to agree that the book is short not even a mention of the Lorentz contraction:
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

Good to know!

Why?

[TheSkepticalOptimist]

99% of the people reading the news won't understand it, so you are not benefiting anyone. It's no like you are going to educate people simply by showing them more math in news reporting. Its not like showing eco Alarmists the math of how the sun is outputting more energy at its peak in a 1000 year cycle is going to convince them that the sky isn't falling.

BTW, Dumageddon has already started and will not be saved by putting more truth into news reporting. The Roman Empire fell because the weak, lazy and stupid overpopulated and grossly outnumbered the philosophers and scientists who could not save them.

When in Rome...

Another thing that bugs me

[harvestsun]

"This rock somehow finds the ideal path to roll down to the bottom of the hill, out of all possible paths! It must be using quantum superposition!"

code

[nten]

Even standard mathematical notation is ambiguous. You can take the same math describing the same relationship, and publications from different fields will use entirely different notation and conventions. For that reason I prefer to convey mathematical relationships using code, whether it is matlab, c, c#, or what have you, all of them can be unambiguously interpreted by a machine. Even the best math paper cannot be parsed by a machine. I sometimes use math notation as a quick sketch on a whiteboard or an IM to someone to say "do something kinda like this but think it out", but if I have already thought it out, I put it in code so it is absolutely clear what I mean. I think hard math, even abstract math would benefit from using a computer language instead of math notation, its old and flawed and not as universal as people like to think. Even if the code isn't in a language you know, the syntax is clearly defined somewhere. If I read a paper in the journal of applied dendromorphology and they re-derive stokes theorem (and try to patent it) and have little tick marks everywhere, how am I supposed to know that "everyone uses those for time derivatives here! what else would you use"? You laugh, but I have seen stranger stuff, much stranger.

Yes, in theory

[GodfatherofSoul]

But, in practice the press is quite happy using the dumbed down mass-appeal approach mixed with sensationalized and outright false representations of the truth. An equation would just get in the way.

A much simpler description

[sjames]

The universe has a limited resolution and the collision detection sux at small scales. As usual, bugfixes are not forthcoming and there will be no refunds.

Mileage will vary

[EngineeringStudent]

The level of math in "general" media is a measure of the anti-intellectualism of a culture. In a highly anti-intellectual culture, more equations are a waste. Don't try to teach a pig to sing. It wastes your time and annoys the pig.

More equations like

[Anonymous Coward]

E = m C .............. ummmmm Hammer???

I wanna see the Schrödinger equation...

[Anonymous Coward]

in the next story about cats that I read. It's all about "...atoms, molecules, and subatomic particles whether free, bound, or localized." :-)

Yes, it's kinda complex...nudge nudge wink wink.

Not For This Article

[Tyler Durden]

The only thing worse than leaving out an equation that will help make your point is including one where it does not. With the latter you either waste time explaining what the equations mean (which takes you away from the thrust of the argument) or lose your audience who stop trying to follow the rest of your argument.

Here the main point of his article is that the subjective nature of collapse that is inherit in the Coppenhagen interpretation is not the only game in town, so people are incorrect when they present this as a necessary consequence of QM. How would talking about equations help make his case?

Actually, it is just a off-by-one error

[roguegramma]

Come on, it is just a off-by-one error, which is common even in software written by above-average-smarts-persons.

And it is definitely smarter to write a bill for one hour of work when you worked from 6am to 6am than to go for no compensation.

Sorry, was meant as a reply to

[roguegramma]

Sorry, was meant as a reply to:

"My (48-year old Thai) girlfriend starts work at 6am and gets off at 6pm. She insists that means she works thirteen hours a day. It is amazing how incredibly dumb the average person is. "

Evidently I'm too dumb to follow a thread on slashdot.

Re:Not equations. Graphs.

[the eric conspiracy]

> This is like arguing about whether kids should be taught calculus in school when they're struggling with basic arithmetic.

It's funny that people who struggle with basic math in school have no problems doing calculations with money or baseball statistics.

It really says to me that the approach is just wrong.

Mathematics is horrible for communication.

[VortexCortex]

Just show any only mildly complex equation with big Sigmas and function symbols and even just one derivation... To an alien. Now, imagine how much they're going to have to learn just to understand that bullshit -- even if they've already mastered all the verbal and written languages of Earth!

If only there were a more verbose system whereby more friendly names could be given to the symbols,
like, "let a equal 10. loop while( a is not equal to zero ){ doThingListedElsewhere() }". Oh if only we had solved this damn problem ages ago with almost EVERY computer programming language in existence.

The answer is to teach a simple (possibly scripting) language like JavaScript, or C, etc. in elementary school IN MATH CLASS. Though not the optimal choice I would vote for JavaScript because its a language every person has the ability to use on the data they most frequently interact with -- The web / HTML.

When I was a pre-teen child, like many others, I taught myself computer programming. I was making games, and spreadsheet software, and even selling them on Compuserve before highschool. Over one summer I independently invented trigonometry. The online help didn't say what SIN and COS functions were used for, and I was trying to find the angle between two points relative to the pixel grid, to turn an enemy ship towards a player -- I needed an angle to pass into the ROTATE( angle ) function before drawing the ship's lines so I made a "slopeRatio(x1, y1, x2, y2)" function that performed better than the built in SIN function because of wasted RAM with my extensive lookup table, and limited required precision, and I returned angles that didn't require multiplying by Pi... That opened the door for many other mathematical discoveries, like distance between points, 3D transforms and rotations, etc.

At the start of the 7th grade when they were trying to re-teach inequalities and order of operations (which I had mastered in 3rd grade in front of an amber screen), I proudly showed my 3D distance formulas to my teacher. She was dismissive and said, "That's nice, we'll cover Pythagoras in another grade, did you do your homework?" NO. THAT was my home work, not some worthless list of add/subtract/multiply/divide to perform by hand -- I INVENTED Trig by myself. She had nothing to teach a child!? I am not gloating, I am pointing out how trivial these revered mathematic discoveries are, and you'd know this too if you ever had to invent any of it yourself. The "amazing" discovery of ratios of the sides of triangles was OBVIOUS to a 12 year old child... There is no such thing as genius, given necessity humans invent, or re-invent as the case may be -- It's not hard, we all do it all the time; Aside: that's why no one searches software patents to use in the PTO database: It's faster to re-invent and yields a more tailored result!

With the revelation that there was a world of mathematics I had mastered parts of myself, I tried not to re-invent the wheels...
I could have saved over a week of summer if I'd have known about c*c = a*a + b*b; instead of deriving it myself. So, I tried cracking open a mathematics book to learn more of the math that I was discovering myself already. However, in place of a For Loop, there was a Sigma Symbol... I didn't understand what I was looking at. Had the equation been verbosely explained in English I would have grokked it immediately since I was already using all of the principals myself. Had there been some simple pseudo-code saying "Do this N times: ...", or
"var a = 10; while( a != 0 ){ a = a - 1; someFunction(); ... }", etc. then as a middle schooler I could have picked up any mathematics book and applied its knowledge. Indeed, once I forced myself to absorb the symbols meanings and map them to C or BASIC I tackled Calculus... Instead of being awestruck at the "elegant genius" I thought, "That's It?! That's what everyone jokes about being so advanced?! I've turned curve equations into

Re:Mathematics is horrible for communication.

[VortexCortex]

Face it, everything has a computer in it! So, not teaching mathematics in an only slightly more descriptive programming language such that it could be immediately applicable would give folks such a better understanding of mathematics and the world, and grant a power to control it as well.

Forgive the self reply, I do not mean to talk down to anyone here, but I fear others would underestimate myself, and misunderstand this statement as a mistake -- Don't get me wrong, I waste no time proofreading, and thus make mistakes in spelling or punctuation, I trust you can understand the meaning regardless of minor imperfections... However, I wish to clarify so as not to be as crystal and not stone.

Not teaching people in a better way that could make all mathematics instantly knowable lets you understand why mathematics is the way it is. Why it is not being taught this better way. Once you understand that this is the information age, and that mathematics is the language of information, and that knowledge is power... You can understand the real world. How would not teaching a better method grant anyone "a power to control" the world? How could fostering ignorance of the language of information with ancient barriers and even tuition fees grant anyone a measure of control? How could not teaching the slaves to read possibly help control them?

Now you may understand why I do not consider myself a member of such a species.

If the article doesnt look like a math thesis ...

[YoungManKlaus]

its fine (eg. provide equations outside the main text in a separate background/proof box), generally a little more facts and less blabla would be very healthy to many articles (esp. in philosophy). At least I personally always aim for most clarity in fewest words (as fewer words reduce the possibility of making mistakes or the appearance of making mistakes because of bad and ambiguous phrasing eg. in two different parts of the text).

"Uncertainty" is a property of all waves

[reve_etrange]

The simplest way to explain the uncertainty principle is this: if you have a wave train of finite length L, then the uncertainty in the wavenumber is at least 2*Pi/L. To see this imagine (or draw) a wave packet which attenuates to zero at either end (like an infinite wave convolved with a Gaussian). Now count the number of waves in the interval L - not so easy, is it?

Mathematically, one would Fourier transform the wave to obtain its frequency (the FT of the wave is a delta function, one point exactly at the frequency of the wave). But the FT of the wave packet has the delta function of the wave, convolved with the FT of the Gaussian - which is also a Gaussian. This leads to a Guassian in frequency space, and thus an uncertainty in the frequency of the wave packet. This type of uncertainty is a property of all wave-type phenomena, from sound waves to probability amplitudes.

Indeed, this is how Feynman treats the principle in Vol III, Ch. 2 of his mighty lecture series.

Is this a serious question?

[daviskw]

Is this a serious question? Would you post Egyptian Hieroglyphic to illustrate some important fact about Egypt 3000 years ago? There are very few Math equations that people understand intuitively and they usually go something like this 5 + 3 = 8. Mathematicians will eat this stuff up. Physicists will appreciate it. Maybe some other math nerds might like it but in the end what will happen is the collective mass of humans will not even bother to shrug their shoulders before they move on.

I love big math formulae and I love equations in stuff but I realize that I am kind of a big nerd that way and the Gods honest truth is that I don't understand most of what I see. I guarantee that not only will most NY Times readers not understand what they are seeing, they will stop reading at that point ant move onto the next article.

No.

[s13g3]

One of the prime edicts of journalism is that you write for your audience, at a level your audience can understand; if you put math in it, less than 1% of the people reading the article, even in the NYT, are going to take anything useful from it besides whatever claim the headline or opening paragraph asserts.

In general, this means that for reporting intended to be consumed by the masses - as opposed to that published in specialized industry journals where certain assumptions can be made about the reader's education level - we write at a 9th to 10th grade reading level. There was even a small amount of noise a while back about one of Obama's speeches that was written even further down at about an 8th grade level.

In effect, this means no, you don't publish articles in the NYT or even WSJ that rely on what is, even for most college-educated readers, NP-hard mathematics that will make no sense to most readers and do absolutely nothing but confuse everyone else, thus failing to communicate the ideas the story is trying to convey in the first place and defeating the purpose of having published it outside of academic journals. You publish in the NYT or the like to reach and spread your message to the widest possible readership, not to reach the handful of specialists in your field who understand the math in question. He's trying to educate people and get them to think, sure, but that doesn't mean that he realistically expect any non-trivial percentage of the intended audience to possess the education or background to be able to make use of anything but generalities and concepts, as opposed to the fine mathematical mechanics underlying his assertion.

I'm better educated than most of my peers - in general, anyway - and quite literate in scientific theories and principles, but I'm also not an engineer, physicist or mathematician, and if you write an article that relies high-order maths to explain its premise, not even I am going to get anything but the gist: I most certainly am not going to grok it any better for the inclusion of math. Of my group of friends, peers and co-workers, only a very small portion of even that bright group of people would benefit from it, at which point you're talking about a readership that is significantly less than 0.25% of the population.

Q.E.D., no, articles written for general or popular consumption that are not inherently targeted at a narrow readership with relevant expertise should not be founded or premised upon the use of math to explain or convey concepts.

Yeah, I was referring to REALLY basic geometry

[sirwired]

When I said "geometry" I meant basic area and volume for 3 and 4 sided polygons, rectangular prisms, plus circles and spheres, along with remembering what a right triangle is. Not anything dealing with trig, proofs, more complicated polygons, etc. I went over this stuff in 6th grade anyway...

My upper limit would probably be 8th-grade algebra, along with a smattering of trig. Conic sections, geometric proofs, most of trig, calculus, stats more complicated than "calculate a mean and median", Linear/DiffEq... fuggedaboutit.

that's rubbish that "mathematicians don't get it"

[KWTm]

I doubt most mathematicians really understand the Pythagorean Theorem. You get so used to theories and their application that you fool yourself into thinking you know them. Take manual long division or multiplication for example. We understand how to line up the numbers and perform the operations but prove to me that it works or *why* it works!

I disagree. Some math concepts are deep, but not Pythagoras. Probably the top 5% of high school graduates understand it, and the only reason the majority of the other 95% don't is that they haven't really tried enough. You really can't understand this animated GIF?

You're talking about mathematicians, who have decided that they will be devoted working with math more than any other field, and you think they don't understand? I can't imagine a single mathematician who can't understand Pythagoras.

And long division -- you don't understand why the numbers line up? How it works? I certainly look down on you for not understanding at this moment, but even then I bet if you thought about it for a bit, you'd understand. It's the decimal system -- meaning that the four digits ABCD represent Ax1000 + Bx100 + Cx10 + D -- and the distributive property of multiplication/division over addition/subtraction.

I can't imagine anyone STARTING to learn to become a mathematician without understanding long division (yes, I mean really grasping it, not just how to write the numbers), much less having become a mathematician.

Daily pay

[AndyCanfield]

As far as I know, she, like most people in Thailand, get paid by the day, not the hour.

H.L. Mencken & Americans & gobbledy-gook

[cundare]

Good luck with all that. Good luck with finding reporters, even highly intelligent ones, capable of inserting, or even intelligently reporting, math in a mainstream news article. In law school -- where one might assume that most of the students are bright enough to do well on the LSAT, which is not all that unlike an IQ test -- my tax-law professor had to promise that the exam would contain arithmetic that that comprised only numbers ending with a string of zeros. When he tried dividing 1000 by 6 in class, there was a revolution in the lecture center. "Wait, no, what? Why do we have to know this stuff? You're going too fast! Wait, let me launch my calculator app."

Americans are repulsed and terrified by arithmetic. Forget about math. Won't happen. Readership would be lost. As far as science or math goes, most people in this country would rather be titillated by the mind-boggling physics explanations on shows like "Fringe" ("Time travel should be relatively easy to understand, Olivia. It's just like lassoing a calf, where the cowboy is a particle accelerator, the calf is a magnetic bottle of entangled positrosn, and the lariat operates in a way analogous to the Arrow of Time. Look at it that way, and there's no question that you could kill your grandfather before you were born.")

Meaning of Statistical Claims, is the big one.

[bbsalem]

Over and over in the press, it is statistical inference that is botched. In the area of medical developments, stories are given coverage that this or that breakthrough has been made when about half way through the story you find that the sample size of a study is very small. Or politicians make some well-known slight of hand with charts that present statistics that support their claims, with a bigger dataset or a different presentation might not support their claims at all.

It doesn't take equations or complex math to get people to recognize flaws in reasoning based on biased or incomplete data. Would people trust the FDA as much as if they were made aware that most of the applications for approvals are made from research studies the developers paid for themselves? The FDA is not funded well enough by Congress to be able to do independent research to support such clams. So it depends on biased research. That is why so many drugs and proceedures have to be pulled from the market after they have been approved by the FDA.

I don't know that I would be as concerned that the press have some math smarts, although that is not a bad thing, but it might be more important that they show some reasoning and inference skills to uncover bias and distortion of the facts. That might require some math skills, but the uncritical passing on of claims is a far more serious problem.

Re: mathematicians are lazy

[NickGnome]

Ask them what the result of division by zero is and they'll tell you they've been goofing off, that they still haven't gotten 'round to defining it. da bums

Yes, the main-stream media should use equations, and words, and diagrams, and graphs/charts, and pictures, and videos.

Quantum mechanics, OTOH, can get nasty. Look at Pauling and Wilson's book. They couldn't bring themselves to choose one style of mathematical notation and stick with it... instead, silently slipping from one to another every few pages, with absolutely no bridging.

energy-momentum-restmass equation

[fritsd]

Interesting, that there was a larger equation,do you have a link for that?

Here: E^2 = p^2 c^2 + m_0^2 c^4
So, when p (momentum) is zero, E^2 = m_0^2 c^4
=> E = +/- m_0 c^2

Linky: http://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation